Dynamical simulation is used in computer animation to assist animators to produce realistic motion, in industrial design (for example to simulate crashes as an early step in crash testing), and in video games.
In computer science, a program called a physics engine is used to model the behaviors of objects in space.
These engines allow simulation of the way bodies of many types are affected by a variety of physical stimuli.
Physics engines are based on the actual behaviors of the world as described by classical mechanics.
The first model which may be used in physics engines governs the motion of infinitesimal objects with finite mass called “particles.” This equation, called Newton’s Second law (see Newton's laws) or the definition of force, is the fundamental behavior governing all motion: This equation allows us to fully model the behavior of particles, but it is not sufficient for most simulations because it does not account for the rotational motion of rigid bodies.
This method requires the Physics engine to solve six ordinary differential equations at every instant we want to render, which is a simple task for modern computers.
However, if we make a few intelligent changes to our system, simulation will become much easier, and our calculation time will decrease.
These equations describe all rotational momentum in terms of the principal axes: The drawback to this model is that all the computation is on the front end, so it is still slower than we would like.
The symmetric sphere makes all of the I terms equal (the Moment of inertia scalar), which makes all of these equations simple: These equations allow us to simulate the behavior of an object that can spin in a way very close to the method simulate motion without spin.
This is a simple model but it is accurate enough to produce realistic output in real-time Dynamical simulations.