Inertia tensors (moment of inertia) code

In summary, the conversation discusses the need for an algorithm to calculate the inertia tensor for shapes in a 2D game. The shapes are represented by closed concave line loops with assigned masses and centers. The speaker has a deadline and is looking for a general solution, having already considered special cases for circles and rectangles. The conversation ends with a request for further elaboration on the inertia tensor and how to work with matrices in C/C++.
  • #1
Aggrav8d
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inertia tensors (moment of inertia) for a game

Hello, physics gurus!

I'm trying to write a little 2D game that uses physics for more dynamism. Part of this game involves shapes bouncing around and reacting to forces, each other, etc. Each shape that can interact is a set of one or more closed concave line loops. (Complex line loops are not allowed.) Each set has an assigned mass and center. What I would like to do is develop an algorithm in C or C++ to calculate the inertia tensor for any of these shapes. I can decompose the shapes into a set of non-overlapping triangles, if that helps. I already have special cases for circles and rectangles who's centers are in the middle of the mass... but I would feel much better if I had a general solution. Sadly I failed my introductory level calculus class and I'm under a bit of a deadline. :yuck:

If anyone of you miracle workers o:) can help me I would be eternally grateful. Thank you in advance!
 
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  • #2
Parallel axis theorem
http://www.ac.wwu.edu/~vawter/PhysicsNet/Topics/RotationalKinematics/MomentInertia.html

http://www.ae.msstate.edu/~masoud/Teaching/SA2/chA3.10_text.html
 
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  • #3
I've seen this before and a few other googles (that's how i found the special case info for rectangles and circles) but I don't understand how to apply this to my situation. Can you please elaborate?
 
  • #4
You know what is the inertia tensor?? and how to work with a matrix in C/C++?
 

1. What is an inertia tensor (moment of inertia)?

An inertia tensor, also known as a moment of inertia, is a mathematical representation of an object's resistance to rotational motion. It takes into account the mass and distribution of mass within an object to determine how difficult it is to rotate that object around a given axis.

2. How is an inertia tensor (moment of inertia) calculated?

The inertia tensor is calculated by using the object's mass distribution and the distance of each mass element from the axis of rotation. The formula for calculating the inertia tensor varies depending on the shape and dimensions of the object, but it generally involves integrating the mass distribution over the object's volume or surface.

3. What are some common applications of inertia tensors (moment of inertia)?

Inertia tensors are commonly used in engineering and physics to analyze and describe the motion of rotating objects. They are also used in robotics and aerospace engineering to design and control the movement of objects in space.

4. Can inertia tensors (moment of inertia) change?

Yes, inertia tensors can change depending on the object's orientation or the axis of rotation. For example, an object's moment of inertia will be different when rotating around its center of mass compared to when rotating around a different point.

5. How can I use a code to calculate an inertia tensor (moment of inertia)?

There are various codes and software programs available that can calculate inertia tensors for different objects. These codes typically require inputting the object's mass distribution and dimensions, and then output the calculated inertia tensor. Some popular codes for calculating inertia tensors include MATLAB, Mathematica, and Python libraries such as SciPy and NumPy.

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