Game Physics Engine Development, 2nd Edition

504 Appendix C Mathematics Summary

Fo rces through an object’s center of mass can be combined using D’Alembert’s

principle:

f =



i

f

i

Forces not through the center of mass also have a torque componen t:

τ = p

f

×f

where p

f

is the position of application of the force , relative to the center of mass.

D’Alembert’s principle also applies to rotations:

τ =



i

τ

i

which includes the torques generated from off-center forces.

The separating velocity of two co lliding objects, v

s

, is related to their velocity

immediately before the collision v

c

by

v

s

=−cv

c

where c is the coefficient of res titution.

C.6 Other Formulas

Hook ’s law related the force of a spring f to its length:

f =−k(|d|−l

0

)



d

where d is the vector from one end of the spring to another.

Simple fluid flow can be