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Game Programming Gems 8 by Adam Lake

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Chapter 2.5. Improved Numerical Integration with Analytical Techniques

Eric Brown

There is a fairly standard recipe for integrating the equation of motion in the context of a game physics engine. Usually the integration technique is based on the Symplectic Euler stepping equations. These equations are fed an acceleration, which is accumulated over the current time step. Such integration methods are useful when the exact nature of the forces acting on an object is unknown. In a video game, the forces that are acting on an object at any given moment are not known beforehand. Therefore, such a numerical technique is very appropriate.

However, though we may not know beforehand the exact nature of the forces that act on an object, ...

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