Ronan

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12 years, 192 days
East Grinstead, United Kingdom

MaplePrimes Activity


These are questions asked by Ronan

I have $ signs suddenly apearing down the side of my document. They are randomly formatting numbers. Don't know how I turned it on. How to undo?  Do they affect calculation accuracy or are they purely dislap formatting

 

 

 


My last series of questions have been to do with animations. Have had some really good help. I am using a rotation type matrix so I can't readilly use the rotate command. That means painfully breaking up the body into its individual components to apply the matrix to. The matrix is derived from some very nolinear functions. I have just included a general Euler rotation matrix here. Have looked inside the rotate command but don't  have enough experience to develop my own. Now I know this sort of command would not be limited to rotating the body as a general 3x3 matrix would transform the body. That would not be a problem, could be useful for other things.

In Mathematica there is a command "GeometricTransformation" that does this.

restart

with(plots):

with(plottools):

NULL

Cylinder := proc (a::list, b::list, dia := .1, colr := "Blue") plots:-arrow(a, b, width = dia, shape = cylindrical_arrow, head_length = 0., head_width = 0.1e-1, colour = colr) end proc

proc (a::list, b::list, dia := .1, colr := "Blue") plots:-arrow(a, b, width = dia, shape = cylindrical_arrow, head_length = 0., head_width = 0.1e-1, colour = colr) end proc

(1)


Body2 := display([point([1, -.2, 0], colour = red, symbolsize = 50, symbol = solidsphere), point([-1, -.2, 0], colour = red, symbolsize = 50, symbol = solidsphere), point([0, 1, 0], colour = purple, symbolsize = 50, symbol = solidsphere), Cylinder([0, 0, 0], [1, -.2, 0], 0.75e-1, "Red"), Cylinder([0, 0, 0], [1, -.2, -0.1e-1], 0.75e-1, "Nautical GrayViolet"), Cylinder([0, 0, 0], [-1, -.2, 0], 0.75e-1, "Red"), Cylinder([0, 0, 0], [-1, -.2, -0.1e-1], 0.75e-1, "Nautical GrayViolet"), Cylinder([0, 0, 0], [0, 1, 0], 0.65e-1, "Green"), Cylinder([0, 0, 0], [0, 1, -0.1e-1], 0.65e-1, "Nautical GrayViolet"), line([0, 0, 0], [.5, 0, 0], colour = red, thickness = 4), line([0, 0, 0], [0, .5, 0], colour = yellow, thickness = 4), line([0, 0, 0], [0, 0, .5], colour = blue, thickness = 4), plots:-textplot3d([.5, 0.5e-1, 0, "X"]), plots:-textplot3d([.1, .5, 0, "Y"]), plots:-textplot3d([0.5e-1, 0, .5, "Z"])], scaling = constrained)

 

NULL

NULL

``

NULL

Rot1 := Matrix(3, 3, {(1, 1) = 1, (1, 2) = 0, (1, 3) = 0, (2, 1) = 0, (2, 2) = cos(w1*t), (2, 3) = -sin(w1*t), (3, 1) = 0, (3, 2) = sin(w1*t), (3, 3) = cos(w1*t)})

Rot2 := Matrix(3, 3, {(1, 1) = cos(w2*t), (1, 2) = 0, (1, 3) = sin(w2*t), (2, 1) = 0, (2, 2) = 1, (2, 3) = 0, (3, 1) = -sin(w2*t), (3, 2) = 0, (3, 3) = cos(w2*t)})

Rot3 := Matrix(3, 3, {(1, 1) = cos(w3*t), (1, 2) = -sin(w3*t), (1, 3) = 0, (2, 1) = sin(w3*t), (2, 2) = cos(w3*t), (2, 3) = 0, (3, 1) = 0, (3, 2) = 0, (3, 3) = 1})

Rot := Rot3.Rot2.Rot1

Matrix(%id = 18446744074366030062)

(2)

NULL

w1 := .35; 1; w2 := .45; 1; w3 := .15

.15

(3)

`~`[evalf](Rot)

Matrix(%id = 18446744074366015718)

(4)

``

NULL

``

NULL

NULL

plots:-animate(plottools:-rotate, [Body2, -w1*t, -w2*t, -w3*t], t = 0 .. 8*Pi, frames = 100);

 

rotate, [Body2, -w1*t, -w2*t, -w3*t]

plottools:-rotate, [INTERFACE_PLOT3D(POINTS(Matrix(1, 3, {(1, 1) = 1.0, (1, 2) = -.2, (1, 3) = .0}, datatype = float[8]), COLOUR(RGB, 1.00000000, 0., 0.), SYMBOL(_SOLIDSPHERE, 50)), POINTS(Matrix(1, 3, {(1, 1) = -1.0, (1, 2) = -.2, (1, 3) = .0}, datatype = float[8]), COLOUR(RGB, 1.00000000, 0., 0.), SYMBOL(_SOLIDSPHERE, 50)), POINTS(Matrix(1, 3, {(1, 1) = .0, (1, 2) = 1.0, (1, 3) = .0}, datatype = float[8]), COLOUR(RGB, .47058824, 0., .44705882), SYMBOL(_SOLIDSPHERE, 50)), POLYGONS([[-0.735435508125000e-2, -0.367717753350000e-1, 0.], [.992645645102007, -.236771775759177, -0.209165228258335e-9], [.993005592857848, -.234972036971338, -0.115881374996887e-1], [-0.699440732540857e-2, -0.349720365471609e-1, -0.115881372905235e-1]], [[-0.699440732540857e-2, -0.349720365471609e-1, -0.115881372905235e-1], [.993005592857848, -.234972036971338, -0.115881374996887e-1], [.994050201935779, -.229748991580870, -0.220419471726219e-1], [-0.594979824747744e-2, -0.297489911566927e-1, 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6.32180968128893]], [[.633327148588615, 4.89050320060954, 6.32180968128893], [-2.36667285464043, -2.10949679990479, .521809683214967], [-2.44194450395682, -2.00432219030132, .433808421285475], [.558055499272224, 4.99567781021301, 6.23380841935944]], [[.558055499272224, 4.99567781021301, 6.23380841935944], [-2.44194450395682, -2.00432219030132, .433808421285475], [-2.47395554646015, -1.89872449432231, .322920361903599], [.526044456768893, 5.10127550619202, 6.12292035997756]], [[.526044456768893, 5.10127550619202, 6.12292035997756], [-2.47395554646015, -1.89872449432231, .322920361903599], [-2.45957251817905, -1.80304035106433, .200000001926036], [.540427485049999, 5.19695964945000, 6.00000000000000]], COLOR(RGB, 1.00000000, 1.00000000, 0.), STYLE(PATCHNOGRID)), MESH([[[-2.00000000322905, -2.00000000051433, .200000001926034], [-2.00459572837855, -1.99803040401983, .200000001926034]], [[-2.00000000322905, -2.00000000051433, .200000001926034], [-2.00395924377148, -1.99723301259337, .198708416786364]], [[-2.00000000322905, -2.00000000051433, .200000001926034], [-2.00289371401770, -1.99673546724239, .197556794937584]], [[-2.00000000322905, -2.00000000051433, .200000001926034], [-2.00151460579941, -1.99659168472588, .196669932476266]], [[-2.00000000322905, -2.00000000051433, .200000001926034], [-1.99997136689115, -1.99681724611051, .196143934711182]], [[-2.00000000322905, -2.00000000051433, .200000001926034], [-1.99843123117443, -1.99738770832032, .196035801661874]], [[-2.00000000322905, -2.00000000051433, .200000001926034], [-1.99706109625184, -1.99824125292325, .196357251222094]], [[-2.00000000322905, -2.00000000051433, .200000001926034], [-1.99600943750207, -1.99928538511744, .197073449344185]], [[-2.00000000322905, -2.00000000051433, .200000001926034], [-1.99539021846883, -2.00040695697829, .198106784848663]], [[-2.00000000322905, -2.00000000051433, .200000001926034], [-1.99527054114253, -2.00148442879169, .199345279799763]], [[-2.00000000322905, -2.00000000051433, .200000001926034], [-1.99566337441848, -2.00240103976796, .200654724052304]], [[-2.00000000322905, -2.00000000051433, .200000001926034], [-1.99652614871577, -2.00305746088513, .201893219003405]], [[-2.00000000322905, -2.00000000051433, .200000001926034], [-1.99776536905199, -2.00338255872975, .202926554507882]], [[-2.00000000322905, -2.00000000051433, .200000001926034], [-1.99924674667521, -2.00334110390592, .203642752629974]], [[-2.00000000322905, -2.00000000051433, .200000001926034], [-2.00080975133403, -2.00293758868706, .203964202190194]], [[-2.00000000322905, -2.00000000051433, .200000001926034], [-2.00228500722112, -2.00221574020830, .203856069140886]], [[-2.00000000322905, -2.00000000051433, .200000001926034], [-2.00351264747019, -2.00125378195296, .203330071375802]], [[-2.00000000322905, -2.00000000051433, .200000001926034], [-2.00435963821144, -2.00015595702432, .202443208914484]], [[-2.00000000322905, -2.00000000051433, .200000001926034], [-2.00473419485564, -1.99904123178791, .201291587065705]], [[-2.00000000322905, -2.00000000051433, .200000001926034], [-2.00459572837855, -1.99803040401983, .200000001926034]]], COLOR(RGB, 1.00000000, 1.00000000, 0.), STYLE(PATCHNOGRID)), POLYGONS([[-2.459572518, -1.803040352, .200000002], [-2.400203330, -1.726635991, 0.77079642e-1], [-2.301659452, -1.676990404, -0.33808418e-1], [-2.173587045, -1.658963247, -.121809680], [-2.028522729, -1.674319144, -.178309968], [-1.880666410, -1.721554952, -.197778640], [-1.744491295, -1.796046901, -.178309968], [-1.633327152, -1.890503202, -.121809679], [-1.558055502, -1.995677811, -0.33808418e-1], [-1.526044460, -2.101275507, 0.77079642e-1], [-1.540427488, -2.196959650, .200000002], [-1.599796676, -2.273364012, .322920363], [-1.698340554, -2.323009598, .433808422], [-1.826412961, -2.341036755, .521809684], [-1.971477277, -2.325680858, .578309972], [-2.119333596, -2.278445050, .597778644], [-2.255508711, -2.203953101, .578309972], [-2.366672854, -2.109496801, .521809684], [-2.441944503, -2.004322191, .433808422], [-2.473955546, -1.898724494, .322920361], [-2.459572518, -1.803040351, .200000001]], COLOUR(RGB, 1.00000000, 1.00000000, 0.), STYLE(PATCHNOGRID)), POLYGONS([[.5404274850, 5.196959649, 6.], [.5997966730, 5.273364010, 5.877079640], [.6983405512, 5.323009597, 5.766191580], [.8264129578, 5.341036754, 5.678190318], [.9714772740, 5.325680857, 5.621690030], [1.119333593, 5.278445049, 5.602221358], [1.255508708, 5.203953100, 5.621690030], [1.366672851, 5.109496800, 5.678190319], [1.441944501, 5.004322190, 5.766191580], [1.473955543, 4.898724494, 5.877079640], [1.459572515, 4.803040350, 6.000000000], [1.400203327, 4.726635990, 6.122920361], [1.301659449, 4.676990403, 6.233808420], [1.173587042, 4.658963246, 6.321809682], [1.028522726, 4.674319143, 6.378309970], [.8806664070, 4.721554951, 6.397778642], [.7444912921, 4.796046900, 6.378309970], [.6333271492, 4.890503200, 6.321809682], [.5580554996, 4.995677810, 6.233808420], [.5260444567, 5.101275507, 6.122920359], [.5404274853, 5.196959650, 5.999999999]], COLOUR(RGB, 1.00000000, 1.00000000, 0.), STYLE(PATCHNOGRID)), SCALING(CONSTRAINED)), -1.75, -3.15, -1.65]

(6)

NULL

``


 

Download Anim_How-3.mw

I was posting some code on a forum tonight. I specificially added # comments to the code. I used Ctrl_c ,Crtl_v. All the # comments were removed including the 2016 grey boxes which appeared as NULL.

Is there away around this. The comments were very important to help in understanding. The pasted code did look readable though.

I also experimented with exporting the code as .txt and opening it in Word. Required loads of editing to make it look presentable, which really opend the door to introuucing errors, also all # coments were removed too.

The forum just has the normal type comments box. Nothing fancy. Actually it is a WordPress Blog. It does accept latex but that is ok for one or two lines. Could be a real mess if 30--40 lines of code go wrong and latex as far as I know can't be copy/pasted back in to Maple.

 

I am experimenting with rotating a group of pionts, lines cylinders etc. the only aminations that  will display are where I put the transformations directly as the point coordinates. This is very tedious. Is there a way around this problem efficiently? Attached worksheet shows problem(s). Ultimately I will have a whole group of objects to rotate.
 

restart

with(plots)

[animate, animate3d, animatecurve, arrow, changecoords, complexplot, complexplot3d, conformal, conformal3d, contourplot, contourplot3d, coordplot, coordplot3d, densityplot, display, dualaxisplot, fieldplot, fieldplot3d, gradplot, gradplot3d, implicitplot, implicitplot3d, inequal, interactive, interactiveparams, intersectplot, listcontplot, listcontplot3d, listdensityplot, listplot, listplot3d, loglogplot, logplot, matrixplot, multiple, odeplot, pareto, plotcompare, pointplot, pointplot3d, polarplot, polygonplot, polygonplot3d, polyhedra_supported, polyhedraplot, rootlocus, semilogplot, setcolors, setoptions, setoptions3d, shadebetween, spacecurve, sparsematrixplot, surfdata, textplot, textplot3d, tubeplot]

(1)

with(plottools)

[annulus, arc, arrow, circle, cone, cuboid, curve, cutin, cutout, cylinder, disk, dodecahedron, ellipse, ellipticArc, exportplot, extrude, getdata, hemisphere, hexahedron, homothety, hyperbola, icosahedron, importplot, line, octahedron, parallelepiped, pieslice, point, polygon, prism, project, rectangle, reflect, rotate, scale, sector, semitorus, sphere, stellate, tetrahedron, torus, transform, translate]

(2)

``

``

``

a1 := proc (t) options operator, arrow; display(line([0, 0, 0], [10*sin(t), 0, 0], colour = red), point([10*sin(t), 0, 0], colour = green, symbolsize = 50, symbol = solidsphere), line([0, 0, 0], [0, 10*sin(t+1.6), 0], colour = orange), point([0, 10*sin(t+1.6), 0], colour = green, symbolsize = 40, symbol = solidsphere), line([0, 0, 0], [0, 0, 10*sin(t+.5)^2], colour = yellow), point([0, 0, 10*sin(t+.5)^2], colour = green, symbolsize = 30, symbol = solidsphere)) end proc

animate(a1, [t], t = 0 .. 2*Pi, frames = 100)

 

c1 := Vector(3, [1, -.2, 0]):

c2 := Vector(3, [-1, -.2, 0]):

c3 := Vector(3, [0, 1, 0]):

c4 := Vector(3, [1, -.2, 0]):

c5 := Vector(3, [-1, -.2, 0]):

c6 := Vector(3, [0, 1, 0]):

c7 := Vector(3, [.5, 0, 0]):

c8 := Vector(3, [0, .5, 0]):

c9 := Vector(3, [0, 0, .5]):

c := [seq(c || n, n = 1 .. 9)]

[Vector[column](%id = 18446744074349586662), Vector[column](%id = 18446744074349586782), Vector[column](%id = 18446744074349586902), Vector[column](%id = 18446744074349587022), Vector[column](%id = 18446744074349587142), Vector[column](%id = 18446744074349587382), Vector[column](%id = 18446744074349587502), Vector[column](%id = 18446744074349587622), Vector[column](%id = 18446744074349587742)]

(3)

Rot := Matrix([[cos(w*t), -sin(w*t), 0], [sin(w*t), cos(w*t), 0], [0, 0, 1]])

Matrix(%id = 18446744074349582806)

(4)

d := seq(Rot.c[n], n = 1 .. 9)

Vector[column](%id = 18446744074349577870), Vector[column](%id = 18446744074349577990), Vector[column](%id = 18446744074349578110), Vector[column](%id = 18446744074349578230), Vector[column](%id = 18446744074349578350), Vector[column](%id = 18446744074349578590), Vector[column](%id = 18446744074349578710), Vector[column](%id = 18446744074349578830), Vector[column](%id = 18446744074349578950)

(5)

``

w := .25

.25

(6)

``

``

[d[1][1], d[1][2], d[1][3]]

[cos(.25*t)+.2*sin(.25*t), sin(.25*t)-.2*cos(.25*t), 0.]

(7)

ff1 := proc (t) options operator, arrow; plots:-display([plottools:-line([0, 0, 0], [d[1][1], d[1][2], d[1][3]], colour = red, thickness = 4)]) end proc

proc (t) options operator, arrow; plots:-display([plottools:-line([0, 0, 0], [d[1][1], d[1][2], d[1][3]], colour = red, thickness = 4)]) end proc

(8)

plots:-animate(ff1, [t], t = 0 .. 5, frames = 100)

 

 

Lend1 := [cos(w*t)+.2*sin(w*t), sin(w*t)-.2*cos(w*t), 0.]

[cos(.25*t)+.2*sin(.25*t), sin(.25*t)-.2*cos(.25*t), 0.]

(9)

ff2 := proc (t) options operator, arrow; plots:-display([plottools:-line([0, 0, 0], Lend1, colour = red, thickness = 4)]) end proc

proc (t) options operator, arrow; plots:-display([plottools:-line([0, 0, 0], Lend1, colour = red, thickness = 4)]) end proc

(10)

plots:-animate(ff2, [t], t = 0 .. 5, frames = 100)

 

``

ff3 := proc (t) options operator, arrow; plots:-display([plottools:-line([0, 0, 0], [cos(.35*t)+.2*sin(.35*t), sin(.35*t)+(-1)*.2*cos(.35*t), 0.], colour = red, thickness = 4)]) end proc

proc (t) options operator, arrow; plots:-display([plottools:-line([0, 0, 0], [cos(.35*t)+.2*sin(.35*t), sin(.35*t)-.2*cos(.35*t), 0.], colour = red, thickness = 4)]) end proc

(11)

plots:-animate(ff3, [t], t = 0 .. 5, frames = 100)

 

``


 

Download Anim_How-1.mw

restart

with(plots)

[animate, animate3d, animatecurve, arrow, changecoords, complexplot, complexplot3d, conformal, conformal3d, contourplot, contourplot3d, coordplot, coordplot3d, densityplot, display, dualaxisplot, fieldplot, fieldplot3d, gradplot, gradplot3d, implicitplot, implicitplot3d, inequal, interactive, interactiveparams, intersectplot, listcontplot, listcontplot3d, listdensityplot, listplot, listplot3d, loglogplot, logplot, matrixplot, multiple, odeplot, pareto, plotcompare, pointplot, pointplot3d, polarplot, polygonplot, polygonplot3d, polyhedra_supported, polyhedraplot, rootlocus, semilogplot, setcolors, setoptions, setoptions3d, shadebetween, spacecurve, sparsematrixplot, surfdata, textplot, textplot3d, tubeplot]

(1)

with(plottools)

[annulus, arc, arrow, circle, cone, cuboid, curve, cutin, cutout, cylinder, disk, dodecahedron, ellipse, ellipticArc, exportplot, extrude, getdata, hemisphere, hexahedron, homothety, hyperbola, icosahedron, importplot, line, octahedron, parallelepiped, pieslice, point, polygon, prism, project, rectangle, reflect, rotate, scale, sector, semitorus, sphere, stellate, tetrahedron, torus, transform, translate]

(2)

``

``

``

a1 := proc (t) options operator, arrow; display(line([0, 0, 0], [10*sin(t), 0, 0], colour = red), point([10*sin(t), 0, 0], colour = green, symbolsize = 50, symbol = solidsphere), line([0, 0, 0], [0, 10*sin(t+1.6), 0], colour = orange), point([0, 10*sin(t+1.6), 0], colour = green, symbolsize = 40, symbol = solidsphere), line([0, 0, 0], [0, 0, 10*sin(t+.5)^2], colour = yellow), point([0, 0, 10*sin(t+.5)^2], colour = green, symbolsize = 30, symbol = solidsphere)) end proc

animate(a1, [t], t = 0 .. 2*Pi, frames = 100)

 

c1 := Vector(3, [1, -.2, 0]):

c2 := Vector(3, [-1, -.2, 0]):

c3 := Vector(3, [0, 1, 0]):

c4 := Vector(3, [1, -.2, 0]):

c5 := Vector(3, [-1, -.2, 0]):

c6 := Vector(3, [0, 1, 0]):

c7 := Vector(3, [.5, 0, 0]):

c8 := Vector(3, [0, .5, 0]):

c9 := Vector(3, [0, 0, .5]):

c := [seq(c || n, n = 1 .. 9)]

[Vector[column](%id = 18446744074349586662), Vector[column](%id = 18446744074349586782), Vector[column](%id = 18446744074349586902), Vector[column](%id = 18446744074349587022), Vector[column](%id = 18446744074349587142), Vector[column](%id = 18446744074349587382), Vector[column](%id = 18446744074349587502), Vector[column](%id = 18446744074349587622), Vector[column](%id = 18446744074349587742)]

(3)

Rot := Matrix([[cos(w*t), -sin(w*t), 0], [sin(w*t), cos(w*t), 0], [0, 0, 1]])

Matrix(%id = 18446744074349582806)

(4)

d := seq(Rot.c[n], n = 1 .. 9)

Vector[column](%id = 18446744074349577870), Vector[column](%id = 18446744074349577990), Vector[column](%id = 18446744074349578110), Vector[column](%id = 18446744074349578230), Vector[column](%id = 18446744074349578350), Vector[column](%id = 18446744074349578590), Vector[column](%id = 18446744074349578710), Vector[column](%id = 18446744074349578830), Vector[column](%id = 18446744074349578950)

(5)

``

w := .25

.25

(6)

``

``

[d[1][1], d[1][2], d[1][3]]

[cos(.25*t)+.2*sin(.25*t), sin(.25*t)-.2*cos(.25*t), 0.]

(7)

ff1 := proc (t) options operator, arrow; plots:-display([plottools:-line([0, 0, 0], [d[1][1], d[1][2], d[1][3]], colour = red, thickness = 4)]) end proc

proc (t) options operator, arrow; plots:-display([plottools:-line([0, 0, 0], [d[1][1], d[1][2], d[1][3]], colour = red, thickness = 4)]) end proc

(8)

plots:-animate(ff1, [t], t = 0 .. 5, frames = 100)

 

 

Lend1 := [cos(w*t)+.2*sin(w*t), sin(w*t)-.2*cos(w*t), 0.]

[cos(.25*t)+.2*sin(.25*t), sin(.25*t)-.2*cos(.25*t), 0.]

(9)

ff2 := proc (t) options operator, arrow; plots:-display([plottools:-line([0, 0, 0], Lend1, colour = red, thickness = 4)]) end proc

proc (t) options operator, arrow; plots:-display([plottools:-line([0, 0, 0], Lend1, colour = red, thickness = 4)]) end proc

(10)

plots:-animate(ff2, [t], t = 0 .. 5, frames = 100)

 

``

ff3 := proc (t) options operator, arrow; plots:-display([plottools:-line([0, 0, 0], [cos(.35*t)+.2*sin(.35*t), sin(.35*t)+(-1)*.2*cos(.35*t), 0.], colour = red, thickness = 4)]) end proc

proc (t) options operator, arrow; plots:-display([plottools:-line([0, 0, 0], [cos(.35*t)+.2*sin(.35*t), sin(.35*t)-.2*cos(.35*t), 0.], colour = red, thickness = 4)]) end proc

(11)

plots:-animate(ff3, [t], t = 0 .. 5, frames = 100)

 

``


 

Download Anim_How-1.mw

I am working with Euler's eqns. of motion. So want to animate the solution. I could do a simple set of spheres along the x, y, z axes  that represent the body or use an imported STL file.  Looking for some guidance on how to approech this. I can import an STL ok. How do I give it an xyz set of axes and then rotate/move these in an inertial frame? I have the equations and solutions already. A reasonable example would be adding an STL of a pendulum to http://www.mapleprimes.com/questions/220957-Non-Simple-Harmonic-Pendulum-Motion#answer235955  to Preben's animation response to a recent post  I placed.

 

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