Integrator8 kommandoer

Transkript

1 Integrator8 kommandoer Rev Filnavn: Int8_Kommandoer.mw Kurver Curve based Commands Argumen ts Output C1 Integration of function along curve kurveint kurveintgo 2 : Fig2 : Curve with weight 3 : Calculation: Integral Go: Integral value C2 Approximation of integration of function along curve kurveintapprox kurveintapproxgo net 2 : Fig2 : Curve with weight 3 : Fig3 : Approximation 4 : Value : Approximated integral and exact value Go: Approximate integral value (needs 'net' input!) C3 The tangential curve integral of a along curve tangkurveint tangkurveintgo 3 : Fig3 : Vector field at curve 4 : Calculation : tangential curve integral Go: Integral value

2 C4 The center of mass of weighted curve C5 kurvecm kurvecmgo The torque from a on weighted curve w. r.t. a point kurvekm kurvekmgo V, pt, V, pt 2 : Fig2 : Curve with weight and center of mass 3 : Value : Total mass and center of mass Go: Center of mass 3 : Fig3 : Curve with weight and and torque 4 : Value : Torque Go: Torque value C6 The moment of of weighted curve w. r.t. a line kurveim kurveimgo pt, e, pt, e 2 : Fig2 : Curve with weight and axis of revolution 3 : Calculation : Moment of 4 : Value : Moment of Go: Moment of C7 The flow of curve along vector field kurveflow T, 3 : Fig3 : Integral curves through curve 4 : Fig4 : Forward flow of curve 5 : Animation : Total flow of curve along 6 : Value : Expression for integral curves

3 Plane områder Planar Domain based Commands Argume nts Output P1 Integration of function along planar planint planintgo 3 : Fig3 : Approximation 4 : Calculation: Integral Go: Integral value P2 Approximation of integration of a function along planar planintapprox planintapproxgo P3 The center of mass of weighted planar P4 plancm plancmgo Wire frame figure traadmodelplan net 3 : Fig3 : Quarter approximation 4 : Value : Approximated integral and exact value Go: Approximate integral (needs 'net' input!) with center of mass 3 : Fig3 : Approximation 4 : Calculation : Total mass of and center of mass Go: Center of mass Fig : Colored wire frame version of planar

4 P5 Wire frame figure traadmodelplangray Fig : Gray wire frame version of planar Flader Surface based Commands Argume nts Output S1 Integration of function over a fladeint fladeintgo wire frame 3 : Fig3 : Parametrized full image 4 : Fig4 : Approximation 5 : Calculation : Surface integral Go: Value of integral S2 Approximation of integration of function over a fladeintapprox fladeintapproxgo net 1: Fig1 : Parameter 3 : Fig3 : Approximation 4 : Value : Approximated integral and exact value Go: Value of approximation (needs 'net' input) S3 The center of mass of weighted fladecm fladecmgo with center of mass 3 : Fig3 : Approximation 4 : Value : Total mass of and center of mass Go: Center of mass

5 S4 The moment of of weighted with respect to a line fladeim fladeimgo pt, e, pt, e with axis 3 : Fig3 : Approximation with axis 4 : Calculation : Moment of Go: Value of moment of S5 The torque from a on weighted w.r.t. a point fladekm fladekmgo V, pt, 1 : Fig1 : Parametrized 3 : Fig3 : Vector field at wire, torque at point 4 : Fig4 : Vector field at full, torque at point 5 : Value : Torque expression for at point Go: Value of torque S6 The flux of a vector field through the fluxint, SurfFlux fluxintgo S7 The flux of the curl of a through the StokesFlux 1 : Fig1 : Parametrized 3 : Fig3 : Vector field at wire 4 : Fig4 : Vector field at full 5 : Calculation : Flux of vector field through Go: Value of flux 1 : Fig1 : Parametrized 3 : Fig3 : Curl of 4 : Fig4 : Curl of at wire frame 5 : Fig5 : Curl of at full 6 : Calculation : Flux of curl of

6 StokesFluxGo field through Go: Value of flux of curl S8 The circulation of a along boundary of the StokesRandInt StokesRandIntGo 1 : Fig1 : Parametrized 3 : Fig3 : Wire frame and full boundary 4 : Fig4 : Vector field at full boundary 5 : Value : Expression of circulation along boundary Go: Value of circulation along boundary S9 The flow of along fladeflow T, 1 : Fig1 : Parametrized around wire frame 3 : Fig3 : Vector field around full 4 : Fig4 : Integral curves through 5 : Fig5 : Forward flow of 6 : Animation : Total flow of along field 7 : Value : Expression for integral curves S1 0 The total wring of a on the fladetotalvrid fladetotalvridgo 1 : Fig1 : Parametrized 3 : Fig3 : Vector field at wire frame 4 : Fig4 : Vector field at full 5 : Fig5 : Wring at wire frame e 6 : Fig6 : Wring at

7 full 7 : Value : Expression of wring and total wring vector Go: Value of total wring S1 1 Wire frame figure traadmodelflade Fig : Colored wire frame version of parametrized S1 2 Gray wire frame figure traadmodelfladegray Fig : Gray wire frame version of parametrized S1 3 Wire frame figure with boundary traadmodelflademed Rand Fig : Wire frame and full boundary Rumlige områder 3D based Commands Argume nts Output Integration of function over 3D rumint rumintgo by boundary s 3 : Fig3 : Parametrized image by wire frame 4 : Fig4 : Approximation 5 : Calculation : Integral Go: Value of integral

8 B2 Approximation of integration of a function over 3D rumintapprox rumintapproxgo 1: Fig1 : Parameter by boundary s 3 : Fig3 : Parametrized image by wire frame 4 : Fig4 : (1/8)-approximation 5 : Value : Approximated integral and exact value Go: Value of approximation (needs 'net' input!) B3 The center of mass of weighted 3D rumcm rumcmgo by boundary s 3 : Fig3 : Parametrized image by wire frame, center of mass 4 : Fig4 : (1/8)-approximation and center of mass 5 : Value : Expression for mass and center of mass B4 The moment of of weighted 3D with respect to a line B5 rumim rumimgo The torque from a on weighted 3D pt, e, pt, e, net Go: Value of center of mass by boundary s 3 : Fig3 : Parametrized wire frame image and axis 4 : Fig4 : (1/8)-approximation and axis 5 : Calculation : Moment of Go: Value of moment of 1 : Fig1 : Parametrized, wire frame 3D, torque at

9 w.r.t. a point rumkm rumkmgo V, pt, V, pt point 3 : Fig3 : Wire frame 3D and torque at point 4 : Value : Torque expression for full 3D around point Go: Value of torque B6 The total divergence of a in 3D divint divintgo 1 : Fig1 : Parametrized image by boundary s 2 : Fig2 : Parametrized wire frame image of 3D 3 : Fig3 : Vector field 4 : Calculation : Total divergence in 3D Go: Value of divergence B7 The total flux of a out through the of a 3D GaussFlux GaussFluxGo 1 : Fig1 : Parametrized image by boundary s 2 : Fig2 : Parametrized wire frame image 3 : Fig3 : Vector field 4 : Value: Total out-flux through (3D )- boundary Go: Value of total out-flux B8 The flow of a 3D along a rumflow T, 1 : Fig1 : Parametrized (3D ) boundary s 2 : Fig2 : Wire frame 3D 3 : Fig3 : Wire frame 3D and 4 : Fig4 : Full 3D and 5 : Fig5 : Integral curves

10 through wire frame 3D 6 : Fig6 : Forward flow of 3D 7 : Animation : Total flow of 3D along field 8 : Value : Expression for integral curves B9 The total curl of a in 3D rumtotalrot rumtotalrotgo 1 : Fig1 : Parametrized (3D ) boundary s 2 : Fig2 : Wire frame 3D and 3 : Fig3 : Curl and wire frame 3D 4 : Value : Expression for total curl of 3D Go: Value of total curl 0 The total wring of a vector field on the boundary of 3D rumrandtotalvrid rumrandtotalvridgo 1 : Fig1 : Parametrized image by boundary s by wire frame 3 : Fig3 : Vector field 4 : Value : Total wring vector for (3D ) boundary Go: Value of total wring of 3D boundary 1 Wire frame 3D figure traadmodelrum Fig : Colored wire frame 3D

11 2 Gray wire frame 3D figure traadmodelrumgray Fig : Gray wire frame 3D 3 (3D ) boundary figure Fig : Colored (3D ) boundary sideflader 4 Wire frame boundary figure traadmodelsideflader Fig : Wire frame (3D ) boundary 5 Gray wire frame boundary figure Fig : Gray wire frame (3D ) boundary traadmodelsideflader Gray