Game Development Reference
Velocity is updated with
p = ˙
Orientation is updated with
is the quaternion form of the angular velocity and t is the duration to up-
Angular velocity is updated exactly the same as linear velocity:
θ = θ
+ θ t
Newton's second law of motion gives us
where m is the mass and p is the position of an object. Or
m − 1 f
in terms of position.
Euler's equivalent for rotation is
I − 1 τ
where I is the inertia tensor and τ is the torque.
The force of gravity is
where g is around 10 m/s 2
on earth, but is often replaced by 20 m/s 2
for added speed
Forces through an object's center of mass can be combined using D'Alembert's
Forces not through the center of mass also have a torque component:
p f ×
where p f is the position of application of the force, relative to the center of mass.