Producing animations with Mathematica 6.0 is as easy as pie
Mathematica 6.0 by Wolfram is a mile stone!
The system allow one to produce with ease animations of mathematical objects like
I was set into animating a cycloid. This is the curve describe by a point on a circle rotating over a line without slipping.
This is actually a very interesting curve that was studied by Galileo, Roberval, Fermat, Descartes, Huygen and Johann Bernoulli in fact he discover this curve is a brachistochrone even more he propose the problem of finding the curve of fastest descent and inaugurating with this problem the variational calculus.
The animation above creates a curve named prolate cycloid one is able to find the meaning of the word prolate in
Websters Dictionary
| 1. | Stretched out; extended; especially, elongated in the direction of a line joining the poles; as, a prolate spheroid; – opposed to oblate. |
and also the definition for
1.(Astron.) Shortened or reduced; – said of the distance of a planet from the sun or earth, as measured in the plane of the ecliptic, or the distance from the sun or earth to that point where a perpendicular, let fall from the planet upon the plane of the ecliptic, meets the ecliptic.
and we also have then the curtate cycloid.
you may also consult Mathworld at
if you like to reproduce the above animations using Mathematica 6.0
you could use the following code
Manipulate[
Graphics[
{{Thick, Yellow, Disk[{x, 1}, 1]},
{Thick, Orange, Circle[{x, 1}, 1]},
{Blue, Thickness[.008],
Line[{{x, 1}, {x - q Sin[x], 1 – q Cos[x]}}]},
{PointSize[Large], Red, Point[{x, 1}]},
{PointSize[Large], Magenta, Point[{x - q Sin[x], 1 – q Cos[x]}]},
If[trace,
{Red, Thick,
Line[
Table[{t - q Sin[t], 1 – q Cos[t]}, {t, 0, x, 0.001}]
]}]}, AspectRatio -> Automatic, Background -> Black,
ImageSize -> {640, 480}, ImagePadding -> 100, AxesOrigin -> {0, 0},
If[va, Axes -> True, Axes -> {True, False}],
AxesStyle -> Directive[Thick, Orange, If[p < 2 Pi, 24, 12]],
PlotRange -> {{-1, 2 p + .5}, {-.5, 2.3}},
If[ticks, Ticks -> {Range[IntegerPart[2 p + .5]], {1, 2}},
Ticks -> {{None}, {None}}]
], {{x, 0}, 0, 2 p, 0.001}, {{q, 1}, 0.01, 5, 0.001}, {{p, Pi},
0.01, 4 Pi,
0.001}, {trace, {True, False}}, {ticks, {True, False}}, {va, {True,
False}}
]
If you like the above posting you may also enjoy this
Building a Geometric figure with Mathematica
This is a blog posting from www.isallaboutmath.com
February 7, 2008 at 7:39 am
um, one small clarification, … not all kinds of animations, just those based mathematical graphs, else … i’m afraid mathematica falls short, like the simulation of a generalization of the three jug problem.
February 27, 2008 at 12:58 pm
I’m pretty sure you could do a nice jug animation in Mathematica too. 3D objects from CAD data or 3D scanner data can be rendered with reflection and transparency now and animated in 3D.