The friction force generated will depend the normal reaction force

424 Chapter 18 Other Types of Physics

The alternative is to resolve a set of contacts at the same time. Rather than calcu-lating the impulse of each in turn, we need to find the impulses of all simultaneously.

The Jacobian is a mathematical construct that says how one contact affects another. It is used to determine the right balance of adjustments to make with the full knowledge of the side effects of any tweak. The Jacobian is a matrix and may be of any size.

All the forces and torques for all objects are combined into one very long vector. There will be three force entries and three torque entries for each rigid body, so the vector will have 6n entries, where n is the number of rigid bodies. In the same way all the accelerations (linear and angular) for all objects are treated as one long vector (again having 6n entries).

18.1 Simultaneous Contact Resolution 425

tion force increases in one direction, the friction force will also increase. There will therefore be an entry in the Jacobian to represent this connection.

Armed with the Jacobian we can formulate the mathematical problem of resolving all contacts at the same time. It has the basic form of

Jf = ¨p