Mathematica: Animated plot sphere as function of time

In summary, to create an animated plot of a sphere as a function of time in Mathematica, you can use the Manipulate function. This allows you to change the radius of the sphere and see the resulting changes in your plot. You can also add elements such as axes, labels, and grids to your plot using the PlotRange, AxesLabel, and GridLines functions. To export your plot as a video or GIF, you can use the Export function. Additionally, you can add a color gradient to your plot using the ColorFunction option in the Plot function, and change the speed of the animation using the AnimationRate option in the Manipulate function.
  • #1
hasidim
15
0
Hi all,

Kinda new to Mathematica.

I have evaluated a function describing a sphere's (or just circle for simplicity) radius over time. I have made a Table of values for the radius over a given time interval, and am able to plot the radius vs time.

How can I make an animated 3D plot of the sphere as it oscillates over time?

Thanks in advance!
 
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  • #2
Here's an example with a circle:
Code: 
Animate[Graphics[Circle[{0, 0}, Sin[t]^2], 
  PlotRange -> {{-2, 2}, {-2, 2}}], {t, 0, 4 \[Pi]}]
 

1. How do I create an animated plot of a sphere as a function of time in Mathematica?

To create an animated plot of a sphere as a function of time in Mathematica, you can use the Manipulate function. This function allows you to dynamically change the values of variables and see the resulting changes in your plot. In this case, you can set the radius of the sphere as a variable and use the Manipulate function to change its value over time, creating an animated effect.

2. Can I add other elements to my animated plot in Mathematica?

Yes, you can add other elements such as axes, labels, and grids to your animated plot in Mathematica. These can be added using the PlotRange, AxesLabel, and GridLines functions, respectively. You can also customize the appearance of these elements by specifying their size, color, and style.

3. How can I export my animated plot as a video or GIF in Mathematica?

To export your animated plot as a video or GIF in Mathematica, you can use the Export function. This function allows you to specify the format and file name of the exported file. For example, to export your plot as a GIF, you can use the following code: Export["myplot.gif", myplot]. This will save your animated plot as a GIF file in your current directory.

4. Is it possible to add a color gradient to my animated plot in Mathematica?

Yes, you can add a color gradient to your animated plot in Mathematica by using the ColorFunction option in the Plot function. This option allows you to specify a function that assigns colors to different values in your plot. You can also use built-in color gradients or create your own custom color functions.

5. Can I change the speed of my animated plot in Mathematica?

Yes, you can change the speed of your animated plot in Mathematica by adjusting the AnimationRate option in the Manipulate function. This option allows you to specify the number of updates per second for your plot. A higher AnimationRate will result in a faster animation, while a lower rate will slow it down.

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