Motion | HP 50g Graphing, 48gII Graphing manual

Motion (8)

Variable

Description

αAngular acceleration

ωAngular velocity (Circular Motion), or Angular velocity at t (Angular Motion)

ω0	Initial angular velocity

ρFluid density

θAngular position at t

	θ0	Initial angular position (Angular Motion), or
	θ0	Initial vertical angel (Projectile Motion)
		Initial vertical angel (Projectile Motion)

aAcceleration

AProjected horizontal area

ar	Centripetal acceleration at r
Cd	Drag coefficient

mMass

MPlanet mass

NRotational speed

RHorizontal range (Projectile Motion), or Planet radius (Escape Velocity)

rRadius

t Time

Velocity at t (linear Motion), or

vTangential velocity at r (Circular Motion), or Terminal velocity (Terminal Velocity), or Escape velocity (Escape Velocity)

v0	Initial velocity
vx	Horizontal component of velocity at t
vy	Vertical component of velocity at t
x	Horizontal position at t
x0	Initial horizontal position
y	Vertical position at t
y0	Initial vertical position

Reference: 3.

534 Equation Reference

Page 470

Image 470

HP 50g Graphing, 48gII Graphing manual Motion

Contents

HP 50g / 49g+ / 48gII graphing calculator Advanced user’s reference manualPage Acknowledgements Printing HistoryPage Contents Alog NamesAlgb Amort 317 →COL DelalarmDelay COL→ 359 Expan FindalarmEXP2POW Expand IDIV2 HaltIBP Iferr List MIN MAXMaxr Not Parity PA2B2Parametric Parsurface 3183 Roll RNDRnrm Rolld 3226 Tail Tabvar→TAG TAN Utpc WireframeUpdir Utpf Contents 514 →ALG Apeek ARM→ ASM ASM→ 610 Toff Tpar AlrmdatCST Exited Expr Iopar MASD.INI Vpar Contents of a Program Understanding Programming Program Results Calculations in a ProgramExamples of Program Actions To enter a program To enter commands and other objects in a programEntering and Executing Programs To store or name a program 3Q!Ì*4#3/* @Ë@Ï To stop an executing program3Q!Ì*4`3/*@Ï @% @Ér # O4 /3 *!Ì Q3 @Ë@Ï Osph K LevelProgram Keys Comments To view or edit a program To switch between entry modesViewing and Editing Programs @%SPH% ˜ Creating Local Variables Using Local VariablesCreating Programs on a Computer `J!%SPH% @%SPH% ˜ Program Comments `OSPHLV K Evaluating Local Names Defining the Scope of Local Variables Compiled Local Variables Creating UserDefined Functions as Programs Key Programmable Description Command Using Tests and Conditional StructuresTesting Conditions To include a test in a program Logical Functions Using Logical FunctionsKeys Programmable Description Command TEST% L Press !%BRCH% !%IF% Using Conditional Structures and CommandsTo enter if then END in a program To enter IFT in a program To enter Ifte in a program or in an algebraic To enter if then Else END in a programPress !%BRCH% @%#IF#% Press !%BRCH% L!%IFTE% To enter Case END in a program Conditional Examples Otst K 26 `52 J %TST% While … Repeat … END Using Loop StructuresUsing Definite Loop Structures To enter Start Next in a program Start Next Structure« … start finish Start loopclause Next … » Press !%BRCH% !%START% To enter Start Step in a program Start Step Structure« … start finish Start loopclause increment Step … » Press ! %BRCH% … %START% To enter for Next in a program For Next Structure« … start finish for counter loopclause Next … » Press !%BRCH% ! %FOR% To enter for Step in a program For Step Structure« … start finish for counter loopclause increment Step … » Press ! %BRCH% … %FOR% « … do loopclause Until testclause END … » Using Indefinite Loop StructuresDo Until END Structure To enter do Until END in a program Duplicates n, stores the value into n To enter While Repeat END in a program While Repeat END Structure« … While testclause Repeat loopclause END … » Press !%BRCH% ! %WHILE% Press ! #MEM# %ARITH% %INCR% or %DECR% Using Loop CountersTo enter Incr or Decr in a program Using Summations Instead of Loops ∑ j Types of Flags Using FlagsSetting, Clearing, and Testing Flags To set, clear, or test a flag Month/day/year format Recalling and Storing the Flag StatesExample Day.month.year format Execute Rclf !L %MODES% %FLAG% L%RCLF% Using SubroutinesTo recall the current flag states To change the current flag states ` 8 J %TORSV% Torsa KTorsv K Press !LL %RUN% %KILL% To singlestep from the start of a programTo turn off the Halt annunciator at any time @·J6 `8 `O%TORSV% !LL%RUN% %DBUG% @·J10 `12 O%TORSV% !LL%RUN% %DBUG% To singlestep when the next step is a subroutineTo singlestep from the middle of a program To cause a userdefined error to occur in a program Trapping ErrorsCausing and Analyzing Errors SingleStep Operations Error Trapping Commands To artificially cause a builtin error to occur in a programTo analyze an error in a program %ERROR% Press !LL %ERROR% !%IFERR% Making an Error Trap« … Iferr trapclause then errorclause END … » Iferr then END Structure To enter Iferr then Else END in a program Press !LL %ERROR% @%IFERR%Iferr then Else END Structure Key Command Description Data Input CommandsUsing PROMPT, Cont for Input Input `OTPROMPT ‰ @·J %TPROM% To respond to Halt while running a program Using Disp Freeze HALT, Cont for InputTo enter Disp Freeze Halt in a program To enter Input in a program Using INPUT, Enter for Input« … promptstring commandline Input OBJ→ … » To respond to Input while running a program %VSPH% To include Input options Commandline cursorposition operatingoptionsTo design the commandline string for Input Cursorposition `O Tinput ‰ To process the result string from InputPress @ Õ ! Ê a @ %TINPU% Using Inform and Choose for Input To set up an input form To set up a choose box `OPHONES ‰ To enter Beep in a program Using Wait for Keystroke InputBeeping to Get Attention To enter Wait in a program Output Using KEY for Keystroke InputData Output Commands OUT% To label a result with a tag Labeling Output with TagsLabeling and Displaying Output as Strings %TTAG% 1.5 ˜1.85 ` To set up a message box Pausing to Display OutputUsing Msgbox to Display Output `OTSTRING ‰ Using Menus with Programs Using Menus for Input Olst ‰ Using Menus to Run ProgramsTo create a menubased application SI% @·J%EIZ% @%%I%% 2*%%I%% !%%E%% Turning Off the Calculator from a Program%% !Ü.37~@6 68 %%I%% !%%Z%% To turn off the calculator in a programPage RPL Programming Examples Fibonacci NumbersFIB1 Fibonacci Numbers, Recursive Version FIB1% !Ü10 N FIB2 Fibonacci Numbers, Loop Version%FIB1% 10 %FIB2% FIB2 program listing%FIB2% Structured programming. Fibt calls both FIB1 and FIB2 Fibt Comparing ProgramExecution TimeTechniques used in Fibt Required Programs 13 %FIBT% Displaying a Binary IntegerPAD Pad with Leading Spaces Techniques used in PAD `OPAD K Preserve Save and Restore Previous StatusPAD program listing Techniques used in Preserve `OPRESERVE K Bdisp Binary DisplayPreserve program listing Techniques used in Bdisp PAD Bdisp program listing `OBDISP K 144 %BDISP% Median of Statistics DataTile Percentile of a list Tile program listing Median Median of Statistics DataTechniques used in %TILE `O%TILE K Techniques used in Median Required Program 18 `12 `˜šš Expanding and Collecting Completely`OMEDIAN K 11 `1 ` Multi program listing Multi Multiple ExecutionTechniques used in Multi `OMULTI K Exco program listing Exco Expand and Collect CompletelyTechniques used in Exco `OEXCO K Ü4 *Y+Z + Minimum and Maximum Array ElementsMNX Minimum or Maximum Element-Version User and system flags for logic control MNX program listing `OMNX K Techniques used in MNX2 MNX2 Minimum or Maximum Element-Version12 `56 `˜šš 45 `1 ` MNX2 program listing Techniques used in Aply Applying a Program to an Array%MNX2% Aply program listing Make sure the flag 1 is clear to begin Ô3†2W†4` ‚Å 3 QA *7 `J %APLY% H#DISP ˜˜ Converting Between Number Bases`OAPLY K Techniques used in nBASE NBASE program listing Verifying Program Arguments 1000 `23 J %NBASE% Names program listing Names Check List for Exactly Two NamesTechniques used in Names `ONAMES K VFY program listing VFY Verify Program ArgumentTechniques used in VFY Ojeff ` Osarah ` Converting Procedures from Algebraic to RPNOben ` %LIST% %²LIST% Techniques used in →RPN →RPN program listing Techniques used in BER Bessel FunctionsXQ3 `%²RPN% %BER% BER program listing`OBER K %BER% !Ü2 Techniques used in Sintp Animation of Successive Taylor’s PolynomialsSintp Converting a Plot to a Graphics Object Sintp program listing Setts program listing Setts Superimposing Taylor’s polynomialsTechniques used in Setts `OSETTS K TSA program listing TSA Animating Taylor’s PolynomialsTechniques used in TSA `OTSA K Techniques used in PIE Programmatic use of matrices and statistics commandsProgrammatic Use of Statistics and Plotting Temporary menu for data input Angle `OPIE K 983 %SLICE% 416 %SLICE% 85 %SLICE% ΑENTER program listing Trace ModeTechniques used in αENTER and ßENTER ßENTER program listing Rootr program listing InverseFunction SolverTechniques used in Rootr `OROOTR K %X²FX% ` 599.5 ` 1 %ROOTR% Animating a Graphical Image@Å@É x †O3.7 Techniques used in Walk `OWALK K Type IntroductionAcos Input/Output Parallel Processing with Lists How Commands Are AlphabetizedOther Provided Details Computer Algebra System Commands and Functions Classification of Operations Library identifier Backup identifierRealnumber time or angle in hoursminutessecond s format Binary integer ACK AbcuvABS Ackall Type Description ACOS2S ASIN, ATAN, COS, Isol Acosh z AcoshASIN2C, ASIN2T, ATAN2S Symb ACOSHsymb ADD Addtmod Alog AddtorealAlgb 10z TVM, TVMBEG, TVMEND, Tvmroot AmortPrincipal Interest Balance Animate ANS ARC Access …µAPPLY Input/OutputApply Archive ARG ARRY→ Access …µARRY→ Input/OutputArit →ARRY Access !¼ ¼is the leftshift of the Skey Asinh ASIN2CASIN2T Symb ASINHsymb ASNAsinh z ACOSH, ATANH, ISOL, Sinh Assume Access … ÃL BIT ASRASR Skey Atan ADDTOREAL, Unassume Symb ATANsymb ATAN2SAtan z ACOS, ASIN, ISOL, TAN Atick Access …µATICKAtanh Atanh z Augment Access …µATTACH Input/OutputAttach #n #m Axes Access …µAUTO Input/Output NoneAuto BAR AXM Access …µAXES Input/OutputAXL Atick xaxis label yaxis label AXL, AXQ AXQBAR AXL, AXM, GAUSS, QXA Basis Access …µBAR Input/Output NoneBarplot Baud Beep Access …µBESTFIT Input/Output NoneAccess … Ã BIN Bestfit Blank Access !L Pict BOX Is the leftshift of the NkeyBins BOX Bytes Access …µBUFLEN Input/OutputBuflen #n1 #m1 #n2 #m2 X1, y1 X2, y2 Cascfg Access … Ã B → RC2P Help CascmdCase Xunit Nunit Symb CEILsymb CeilCentr FLOOR, IP, RND, Trnc Chinrem Cholesky CHR Command ResultChoose NUM, POS CircCksm REPL, SIZE, SUB Cllcd ClearClkadj Closeio Clvar CLΣClusr Cmplx COL →COLCOL→ Collect COL+Colct Symb1 Symb2 CON ColσComb Symb COMBsymb ,m COMBn, symb COMBsymb ,symb Carray constant Name CondRarray constant IDN Conj Access …µCONIC Input/Output NoneConic Constants ConlibConst Rarray Carray Symb CONJsymb Corr ContConvert X1unitssource X2unitstarget X3unitstarget Cosh Access FlagsCOS COV Cswp CrdirCross …µCR Cylin CurlCyclotomic COL+, COL-, Rswp Date →PXDarcy #n, #m Dbug →DATEDATE+ →date Decr DdaysDEC « program » or program name Define DedicaceDEF Result See also Degree DelalarmDEG Name=exp Namename Name =expname Delkeys DelayRCLALARM, Stoalarm CR, OLDPRT, PRLCD, PRST, PRSTC, PRVAR, PR1 Depth Access …µDEPND Input/OutputDepnd Xkey1, ... ,xkey n Desolve DerivDervx Detach Access …µDETACH Input/OutputDET Attach Diagmap DIAG→→DIAG Diff Diffeq Disp Access …µDIFFEQ Input/OutputDIR Obj List DispxyDistrib FREEZE, HALT, INPUT, Prompt DIV2MOD DIVDIV2 CURL, Hess Divpc DivisDivmod DIV2 Until testclause END TAYLOR0, TAYLR, SeriesDERIV, DERVX, DESOLVE, ∂ END Dolist ErrorDoerr Dosubs List List n « program » Results Command Name List n+1Domain SIGNTAB, Tabvar DOLIST, ENDSUB, NSUB, Stream List « program » Command NameDOT CNRM, CROSS, DET, Rnrm Draw Access …µDRAWAccess …µDRAX Input/Output None DRAW3DMATRIX DROP2 DroiteDrop Lagrange DUP DropnDtag DUP2 Dupdup Dupn Egcd EditEditb Else EGVEgvl END EPSX0 EndsubENG Sign mantissa E sign exponent EQ→ EqnlibEQW Erase Errn ERR0Errm Euler Obj See above EvalExlr →NUM Ex,y = excosy + iexsiny EXP&LNEXP Expan EXP2HYPEXP2POW COLCT, EXPAND, ISOL, QUAD, Show ExpandExpandmod Result X2+X Expm ExpfitExpln Eyept Factor F0λFact …µF0λ Modsto FactormodFactors FAST3D Access …µFANNINGFanning Fcoef Access …µFAST3D Input/Output NoneAccess ! Test LL FC ? C FC? CF, FC?, FS? FS?C, SF FdistribFFT Distrib Filer FindalarmAccess …µFINISH Finish FONT6 FlashevalFloor Xunit Nunit Symb FLOORsymb FONT→ FONT7FONT8 →FONT For Freeze FourierFree Xunit Yunit Symb FPsymb Display Area Value Code FrootsFS? CLLCD, DISP, Halt CF, FC?, FC?C, FS?C, SF FS?CFunction Exlr Access …µFUNCTIONFxnd Gbasis GammaGauss AXQ, QXA GET GCDGcdmod GCDMOD, EGCD, IEGCD, LCM GETI, PUT, Puti GetiObjget GET, PUT, Puti GORGrad #n #m Grob1 Greduce GramschmidtGraph DEG, RAD Gridmap Access …µGRIDMAP Input/Output NoneAccess …µ→GROB →GROB Gxor GrobGrobadd →LCD, LCD→ Halt HadamardHalftan GOR, REPL, SUB →HEADER HeadHEADER→ Help HEX HermiteHess CURL, DIV Hilbert Histogram HMS Access …µHISTPLOT Input/Output NoneHistplot HMS+ … & 9L HMS + HMS→→HMS … &9L HMS → Iabcuv HomeHorner IBP IbasisIbernoulli ABCUV, Iegcd Results See also IchinremIDN Chinrem DIV2, Iquot IDIV2Iegcd Ax+by=c ELSE, END, IFERR, then IferrCase ∑ Y k e Ifft Ilap IFTIfte Obj It depends …ßIM ImageLAP, Lapl Rarray Carray Symb IMsymb Inform IncrIndep Global Global xstart xend Input ResetsTitle Format Resets Init → vals Init PROMPT, STR→ Stack prompt Commandline prompt ResultINT INV IntegerIntvx INTVX, Risch Iquot Command INVMOD2 ResultInvmod Isom IremainderIsol Symb1 Global Symb2 Mkisom ISPRIME?Jordan NEXTPRIME, Prevprime KEY KERKerrm BASIS, Image →KEYTIME Access …µKEYEVAL Input/OutputKeyeval Kill KEYTIME→Kget Label LANGUAGE→ Access …µ→LANGUAGE Input/OutputLagrange →LANGUAGE Last LAPLapl Objn Obj1 →LCD LastargLCD→ LCM Lcxm Ldec Libs LgcdLibeval HERMITE, Tchebycheff LIN LimLimit Title, nlib, nport, ...,title, nlib, nport Linfit LineΣline Model Form of Expression LIST→ LininLinsolve →LIST Σlist ListΠlist Access …¹ ¹is the rightshift of the Qkey LNP1 LnameLncollect Ln x + LocalLOG Symb LNP1symb Access !Ø Input/Output Logfit LSQ Access …µLR Input/OutputFull Command and Function Reference 3139 Intercept x Slope x DET, INV LvarMAD Lname Mant Access …µMAP Input/OutputMain MAP ↑MATCH Access …µ↓MATCH Input/OutputAccess …µ↑MATCH Symb Symb symb MAX MathsMatr Symb Symb , symb Mcalc MaxrMaxσ Input/Output See also Menu MeanMEM BINS, MAXΣ, MINΣ, SDEV, TOT, VAR Menuxy RCLMENU, Tmenu Minehunt MergeMIN MENU, Tmenu Minit MINIFONT→→MINIFONT Minr Mkisom MinσMitm 00000000000E-499 Modular MODModsto Mod y Msgbox MolwtMroot Name Or xunit String Mslv Msolvr →NDISP MultmodMuser EQNLIB, MCALC, MINIT, MITM, MROOT, MSLV, Muser Ndupn Access …ß NEG ßis the rightshift of the 1keyNdist NEG Nextprime NewobNext Not Access ! Test L not Is the leftshift of the NkeyNIP Noval NUM Nsub→NUM …µNΣ OBJ→ NumxNumy Oldprt OCTOFF … &NL OBJ → Openio Access …µOLDPRTAccess …µOPENIO Memory Directory Lorder is the leftshift of the Nkey OrderOver Global1 ... globaln Parametric P2CPA2B2 Xmin, ymin, xmax, ymax, indep, res, axes, ptype, depend Access …µPARITY Input/Output Parity Parsurface Partfrac Pcoef PathPcar Home directoryname 1 ... directoryname n Pcov Access …µPCONTOUR Input/Output NonePcontour Perm PdimPerinfo Xmax, ymax Pgdir PertblPeval Pick Picture Pict Command Puts the name Pict on the stackPict Pinit Pixoff Access …µPKTPIX? Pixon Pmax PlotPlotadd Pmin Finds the minimal polynomial of a matrix PminiPolar An nxn matrix a POP Access …µPOLARPolynomial Form of Current Plotting Action Equation Potential Input An expression raised to a powerPOS Powexpand Powmod PR1 …µPR1 PredvPredx Object Predy Preval Prompt PrevprimePrlcd Promptsto Global→ ProotPropfrac Prompt STO Prvar PrstPrstc Name Name1 name2 Nport global Psi PsdevPSI MEAN, PCOV, PVAR, SDEV, TOT, VAR Purge PtaylPtprop Symb String or x or xunit or name Global Global1 ... globaln PushPUT CLEAR, CLVAR, NEWOB, Pgdir Obj put List This command sequencePuti Obj put List Name MEAN, PCOV, PSDEV, SDEV, VAR PvarPvars Pview Access …µPVARS Input/OutputNport namebackup Memory Pwrfit + c/d*i PX→C→Qπ + c/ d Quad̟ + c/ d* ̟ LQ, LSQ Arithmetic, !ÞPOLYNOMIAL !« QuotQuote Quotient of the Euclidean division Rand QXARAD Rank Ratio Access …µRATIORanm LQ, LSQ, QR Rcij RceqRCI Steq Rclalarm RCL Rclkeys FINDALARM, StoalarmRclf Rclmenu Rcws RclvxRclσ RDM …ßL RE RDZCOMB, PERM, Rand Recv RecnRect REsymb Quot RemainderRename New name Old name Repl ReorderRepeat END, While String target Plot Type Default IntervalRES String String result Resultant RestoreBackup To restore a Slopefield Risch RevlistRewrite RKF Rkferr Is the rightshift 3key Problem for a differential equationRkfstep RLB, RR, RRB RLBRND RNDsymb Rolld RnrmRoll Romupload ROW RootROT 3207 →ROW ROW+ROW→ RRB Access … ÃL Byte RRB Is the rightshift of the 3keyRPL RL, RLB, RRB Rref Rref Rrefmod RRK − 2 t + t 2 Rrkstep RKF, RKFERR, RKFSTEP, RRK, Rsberr RsberrRSD Rules Access … Ã R → BRswp DET, IDN 180/̟x Same→R, IM, RE →Dsymb Scale Access …µSCALEH Input/OutputSbrk Scaleh AUTO, SCALEH, Xrng ScatrplotScatter SCI Access …µSCATTER Input/Output NoneSchur Sclσ Sdev SconjScroll Send DOSUBS, Stream SEQSeries Server Seval Sigma ShowSidens X1/cm3 Sigmavx Access !ÖDERIV LAccess !ÖDERIV LL Sign SIGNsymb SigntabSIMP2 ABS, MANT, Xpon Sincos SimplifySIN Sin z Size SinhSinv Sinh z String Integer List Vector SLBSlopefield Symb Grob NEG, SCONJ, Sinv SnegSnrm Solve Solveqn Sort SolverSolvevx Square Analytic Function Returns the square of the argument SphereSrad SQsymb COND, SNRM, Trace SRBSrecv ASR, SL, SLB, SR SST Access …µSRECVSrepl SST↓ Step StartSTD Steq Access …µSTIMEStep Stime STO StoalarmAccess Input/Output Buflen Stokeys Access …µSTOFStof Óis the rightshift of the 9 key STO+ StoreStovx STO/, + →STR StoσSTR→ DTAG, EQ→, LIST→, OBJ→, →STR Sturm StreamStrm List Obj Result SUB SturmabStws Sturmab X1, y1 X2, y2 SubstSubtmod CHR, GOR, GXOR, NUM, POS, REPL, Size Swap SVDSVL DIAG→, MIN, SVL SYST2MAT SysevalSylvester X, symb Tabval100 y Symb 1, symb Tail Tabvar→TAG →ARRY TAN2SC TANTAN2CS2 Tan z Tanh z TAN2SC2Tanh TANHsymb Tchebycheff TAYLOR0Taylr HERMITE, Legendre Tests TcollectTdelta TDELTAsymb1, symb2 Text TevalTexpand Then →TIME TicksTime Tinc TINCsymb1, symb2 TlinTline SIMPLIFY, TCOLLECT, Texpand Trace TmenuTOT Tran Effect TransioTrig BAUD, CKSM, Parity Trigsin TrigcosTrigo Trigtan CONJ, Tran TRNTrnc TRNCz TruncTruth TRNCsymb Tstr Access …µTRUTH Input/Output NoneTsimp Tvmbeg TvarsTVM Tvmend Ubase Builtin CommandsType Object Type Number User objects Unassign UfactUFL1→MINIF Unassume Unpick Unbind→UNIT Updir UnrotUntil Utpc UTPF, UTPN, Utpt UtpfUtpn UTPC, UTPN, Utpt UVALsymb UtptUval X1, x2 Flag -16 clear Rectangular mode Flag -16 set Polar mode € yCoordinate System -16, Complex Mode X1, x2, ..., xn Xn-2 Vandermonde VAR VER Access …µVERSION Input/OutputVars Version Visit Variable name Contents opened in the command line EditorVariable name Contents opened in the most suitable Editor Visitb Wait Access ! L in Wait Is the leftshift of the NkeyVtype While testclause Repeat loopclause END WireframeWhile While Repeat Wslog ΣX2 Access …µWSLOGAccess …µΣX Input/Output Log4 ... log1 Xget ΣX2Xcol Xmit XOR Access …µXMITXnum XPONsymb XponXput MANT, Sign Xrecv Command XQ.3658 Results 1829/5000Command XQ.3658 Results √19/142 Xrng Xserv Access …µXSENDXsend Input/Output RPN ΣXY XvolXxrng ΣX*Y Ycol ΣY2ΣY2 …µΣY AUTO, PDIM, PMAX, PMIN, Xrng YrngYslice Zeros YvolYyrng EYEPT, XVOL, XXRNG, YYRNG, Zvol Zfactor PowerAccess Q Zvol Zsymb Where√ Square Root Symbz SQ, , Isol ? Undefined Access …Á Áis the rightshift of the UkeyIntegrate Lower limit, upper limit, integrand, name Sigma Plus ∞ InfinitySummation Results -π/2 Sigma Minus Access …µΣ+ Input/OutputAccess …µΣ Input/Output X 2, …, x m 1, …, x 1 m x n 1, … , x n m 14159265359… ∂ DerivativeFactorial Symb Name Xunit Xy/100 PercentUnit attachment Symb,x Type Object Description « » Program delimitersLess than ≤ Less than or Equal #n1 #n2 Greater than ≥ Greater than or Equal ≠ Not equal Multiply ≠ symb + Add Subtract Divide = Equal Y1/unit == Logical Equality DEFINE, RCL, →, STO Store→ Create Local … É Semicolon CLEAR, DROP, DROPN, DROP2 Points to note when choosing settings CAS SettingsSelecting CAS Settings CAS directory, Casdir Computer Algebra System Compatibility with Other Calculators Using the CASExamples and Help Extending the CAS Algebra commands, …× Computer algebra command categories listed by menuArithmetic commands Arithmetic Integer commands, !ÞINTEGER Other Arithmetic commands, !Þ Arithmetic Modulo commands, !Þ ModuloArithmetic Permutation commands, !Þ Permutation Calculus commands Create, !Ø Create Exp and Lin commands, !ÐMatrixrelated commands Operations, !Ø Operations Linear Applications, !Ø Linear Appl Quadratic form, !Ø Quadratic FormLinear Systems, !Ø Linear Systems Eigenvectors, !Ø Eigenvectors Other Trigonometry commands, …Ñ Symbolic solve commands, !ÎTrigonometry commands Hyperbolic, …Ñ Hyperbolic Base conversion tools, !Ú Base Convert commands, !ÚUnit conversion tools, !Ú Units Tools Trigonometric conversions, !Ú Trig Conv Other CAS operations, …µ Matrix convert, !Ú Matrix Convert CAS utility operations CAS menu commands, …µThese commands display menus or lists of CAS operations Equation Reference Equation Reference FLUIDS, 24 *********************3 Σcr Critical stress Σmax Maximum stress Columns and BeamsVariable Description Internal bending moment at Equations Elastic Buckling 1Eccentric Columns 1 Example Equation Simple Deflection 1Simple Slope 1 Simple Shear 1 Solution V=624.387lbfSimple Moment 1 Cantilever Moment 1 Cantilever Deflection 1Cantilever Slope 1 Solution V=200lbf Equation Reference Cantilever Shear 1 Relative permeability ElectricityRelative permittivity Ohm’s Law and Power 2 Coulomb’s Law 2 Solution I1=5.6250A Wire Resistance 2Solution V1=80V Voltage Divider 2 Series and Parallel C 2 Solution R=0.175Series and Parallel R 2 Capacitive Energy 2 Solution V=50VSeries and Parallel L 2 Inductive Energy 2 DC Capacitor Current 2 RLC Current Delay 2Solution q=0.0020C Equation Reference Capacitor Charge 2 RC Transient 2 Solution V=3.2968VDC Inductor Voltage 2 RL Transient 2 Plate Capacitor 2 Solution I=0.0072AResonant Frequency 2 Cylindrical Capacitor 2,19 Solenoid Inductance 2 Toroid Inductance 2 Sinusoidal Current 2 FluidsSinusoidal Voltage 2 Reynolds number Pressure at Depth 3Bernoulli Equation 3 Initial and final velocities Flow with Losses 3 Forces and Energy Flow in Full Pipes 3 Linear Mechanics 4 Hooke’s Law 4 Angular Mechanics 4Centripetal Force 4 Law of Gravitation 4 1D Elastic Collisions 4Drag Force 4 MassEnergy Relation 4 Gases Ideal Gas Law 5 Isothermal Expansion 5 Solution Vf=21Ideal Gas State Change 5 Polytropic Processes 5 Real Gas Law 5 Real Gas State Change 5 Heat Transfer Kinetic Theory 5 Conduction 6 Heat Capacity 6Thermal Expansion 6 Convection 6 Conduction + Convection 6 Fba MagnetismBlack Body Radiation 6 Ia, Ib Straight Wire 7 Force between Wires 7 Magnetic B Field in Toroid 7 Solution B=0.0785TMagnetic B Field in Solenoid 7 Motion Projectile Motion 8 Linear Motion 8Object in Free Fall 8 Terminal Velocity 8 Angular Motion 8Circular Motion 8 Escape Velocity 8 Optics Law of Refraction 9 Critical Angle 9 Brewster’s Law 9 Spherical Refraction 9 Solution n2=1.5000Spherical Reflection 9 Thin Lens 9 Oscillations Example Given L=15cm MassSpring System 10Simple Pendulum 10 Simple Harmonic 10 Conical Pendulum 10Torsional Pendulum 10 Plane Geometry Equations Example Circle 11Ellipse 11 Rectangle 11 Regular Polygon 11 Circular Ring 11 Triangle 11 Solid Geometry Cone 12 Cylinder 12 Parallelepiped 12 Sphere 12 Solid State Devices Drawn gate length Nmos Transistors, or Saturation current densityDrawn mask length PN Step Junctions, or Channel length JFETs PN Step Junctions 13 Nmos Transistors 13 VDS Bipolar Transistors 13 JFETs 13 Xdmax = ⋅ Vbi VGS + VDS Minimum principal normal stress Stress AnalysisMaximum principal normal stress Stress on an Element 14 Normal Stress 14Shear Stress 14 Mohr’s Circle 14 Example Longitudinal Waves 15 WavesTransverse Waves 15,1 Sound Waves 15 References Page Development Library Obj1 … objn Symb Obj1, ...,objn Development Library Command ReferenceObj String Development Library String Obj BetaTestingString Obj Debug string Error list Code String Library n String Error list Edited stringLibrary Object String LC~C Ey,z.Et →LST Obj … obj Obj 1, ...,obj n Pokearm Obj 1 … obj n Obj 1, ...,obj n Returns →S2String1 String2 String Global Crlib Create Library Command Xlib Extension program Starting Masd Masd The Machine Language and System RPL CompilerIntroduction Modes Error messages Message Description ErrorsFormat of the error list Links Labels Extable Constants Expressions Operator Priority Macros and includes Directive Description Filename conventionsCompilation directive !DBGINF directive Docstr Bit registers Saturn ASM modeCPU architecture Skips Other notesNew instructions Skips instructions Equivalents These instructions Are equivalent to Tests Saturn instructions syntax Syntax Example Syntax Example DReg=hh See above. This is only valid in emulated Saturn Places the value of Exp in the code, on x nibbles CARRY0 003AA Autousertest ARM mode ARM architecture Instruction set Description Form Operation Assembler Action Flags REG a Armsat instructionOffset Element REG B REG C REG D REG R0 REG R1 REG R2 REG R3 REG R4 Reals and system binary System RPL modeInstructions Unnamed local variables Token Description DefinesTokens Code LC 001 Gosbvl Outcinrtn ?CBIT=1.6 Turnmenuoff LC 80100 Armsat Disassemblers Level Nop Entry Point Library ExtableLibrary String String 1, ...,string n Message Meaning # hex Error and Status Messages A1Messages Listed Alphabetically C0C A2 Error and Status Messages Error and Status Messages A3 A4 Error and Status Messages Σdat Error and Status Messages A5 A6 Error and Status Messages C0B Error and Status Messages A7C0E C0D A8 Error and Status Messages Error and Status Messages A9 # hex Message General Messages A10 Error and Status Messages # hex Message Error and Status Messages A11 OutofMemory Prompts Object Editing Messages Stack Errors and MessagesA12 Error and Status Messages Equation Writer Application Messages Array Messages # hex Message FloatingPoint ErrorsError and Status Messages A13 Statistics Messages Mode and Plot Input Form Prompts A14 Error and Status Messages Error and Status Messages A15 # hex Message 70F A16 Error and Status Messages 73F Error and Status Messages A17 75F A18 Error and Status Messages 78F Error and Status Messages A19 A20 Error and Status Messages Advanced Statistics Messages Error and Status Messages A21 80F A22 Error and Status Messages 82F Error and Status Messages A23 85F A24 Error and Status Messages 87F HP Solve Application Messages Error and Status Messages A25Statistics Help Messages Time Messages # hex Message Unit ManagementPrinting Programmer’s Doerr Error and Status Messages A27 A28 Error and Status Messages System Flags Choose Box Prompts Error and Status Messages A29 A30 Error and Status Messages Error and Status Messages A31 A32 Error and Status Messages Prompts Error and Status Messages A33 A34 Error and Status Messages Error and Status Messages A35 Statistics Prompts Time and Alarm Prompts A36 Error and Status Messages Error and Status Messages A37 Symbolic Application Prompts A38 Error and Status Messages Error and Status Messages A39 Plot Application Prompts A40 Error and Status Messages Error and Status Messages A41 A42 Error and Status Messages Solve Application Prompts Error and Status Messages A43 A44 Error and Status Messages Error and Status Messages A45 CAS Messages A46 Error and Status Messages Error and Status Messages A47 DF0A DF0B DF0C DF0D DF0E DF0F A48 Error and Status MessagesFiler Application Messages DF1A DF1B DF1C DF1D DF1E DF1F Error and Status Messages A49 Constants Library Messages Minehunt Game Prompts A50 Error and Status MessagesEquation Library Messages MultipleEquation Solver Messages Financial Solver Messages Error and Status Messages A51Periodic Table Messages Development Library and Miscellaneous Messages A52 Error and Status Messages Units Tables of Units and Constants B1 B2 Tables of Units and Constants Tables of Units and Constants B3 B4 Tables of Units and Constants Tables of Units and Constants B5 Constant Full Name Value in SI Units Properties of Elements B6 Tables of Units and Constants Not used System FlagsFlag Description System Flags C1 C2 System Flags System Flags C3 C4 System Flags System Flags C5 C6 System Flags System Flags C7 Internal use only /0 occurred C8 System Flags User Flags System Flags C9Page Reserved Variables D1 Contents of the System Reserved Variables ΒENTER Reserved Variables D3 Exited D4 Reserved Variables Reserved Variables D5 N1, n2 MHparMpar Nmines BAR, etc Reserved Variables D7 Prtpar D8 Reserved Variables S1, s2 Reserved Variables D9 NUMX, Numy Parameter Description Default Value CommandTo use for input into the table D10 Reserved Variables Reserved Variables D11 Var1 var2 … varmStatistical Matrix for Variables 1 to m EXPFIT, PWRFIT, or Logfit D12 Reserved Variables Casdir Reserved Variables Modulo D14 Reserved Variables Technical Reference E1 Object SizeObject Type Size bytes E2 Technical Reference Symbolic IntegrationPattern Antiderivative Technical Reference E3 →DEF Expansions E4 Technical Reference Order Operation Technical Reference E5 International Standard publication No. ISO 31/l197 8 E E6 Technical Reference General rules for parallel processing Group 1 Commands that cannot parallel processGroup 2 Commands that must use Dolist to parallel process Parallel Processing with Lists F1 Group 4 ADD and + Group 5 Commands that set modes / statesGroup 6 Oneargument, oneresult commands F2 Parallel Processing with Lists Group 9 Multipleresult commands Group 7 Two argument, one result commandsGroup 8 Multipleargument, oneresult commands Group 10 Quirky commands Using Dolist for Parallel Processing F4 Parallel Processing with Lists $ & F $ & C$ & D $ & + @ & ³ @ & O Keycode Keystroke Definition¥ ! &I ~@ & O Keyboard Shortcuts G3 ~@ & Í @ &†@%VARNAME% = varname G4 Keyboard Shortcuts MenuNumber Table H1 Menu NumbersSyntax Example Menus 0 through H2 The MenuNumber Table MenuNumber Table H3 Menus 118 through H4 The MenuNumber Table MenuNumber Table H5 Menus 178 throughBuiltIn Library Menus Page + key Command MenuPath TableKey ALPHARS2 MTH NXT Prob Command Type Library Size Keys Menu First I2 The Command MenuPath Table «MODULAR» Addtoreal MTH ListArith Modul CAT Algb I4 The Command MenuPath Table PRG NXT LS&MODE FlagPRG Test NXT NXT PRG NXT Modes Flag Chinrem CHR I6 The Command MenuPath Table RS&TIME NXT CAT DelalarmPRG NXT NXT Time Alrm Delay PRG NXT NXT Time NXT I8 The Command MenuPath Table MTH Matrx NXT PRG NXT NXT Error Iferr«POLYNOMIAL» EGV Else I10 The Command MenuPath Table I11 I12 The Command MenuPath Table PRG Brch NXT Calc Deriv NXT«INTEGER» «DIFF» NXT NXT I14 The Command MenuPath Table I15 I16 The Command MenuPath Table I17 I18 The Command MenuPath Table I19 I20 The Command MenuPath Table I21 I22 The Command MenuPath Table I23 I24 The Command MenuPath Table I25 I26 The Command MenuPath Table I27 I28 The Command MenuPath Table CAT Vtype Matrices Creat NXT NXT MTH Matrx Make NXT NXTDUP Menuxy Version XLIB~ Alphalse I30 The Command MenuPath TableSLV NXT MTH NXT Const «CONSTANTS» PRG Test «TESTS» NXT ΣlineΣlist →ALG I32 The Command MenuPath Table Ascii Character Codes and Translations J1 Code DescriptionCharacter Codes Code Trans. Description J2 Ascii Character Codes and Translations Index Alpha keyboard Calculator 59, 531 375 Preserving calculator status Flags 132 Last argument Memory Nested structures 545 Programs Range 3115 Serial communications 237, D3 Tagged objects UPs

Motion (8)

Variable

Description

Drag coefficient

534 Equation Reference