Dynamics cheat sheet

14.2 3D Not Using vehicle dynamics notations
Nasser M. Abbasi
3d_1.vsd
May 26, 2011
z
F z
Linear force
torque
Linear velocity
v
v x
v y
v z
angular velocity
v z
F x
x
I
v x
x
x
z
z
y
y
F y
F
Forces, Torques, linear
velocities and angular
velocities for a general 3D
rigid body
I xx I xy I xz
I yx I yy I yz
F d p dt d mvm d v m dt dt
a y z v x x v z
a
a x y v z z v y
v y
y
x
y
z
F x
F y
F z
x
y
z
linear momentum
a z x v y y v z
The derivation of the above is given next, but it uses the standard formula given by
d
A d
A A
dt dt resolved
This is in the
inertial frame of
reference
This is the same A, but its components
are with respect to the body fixed
coordinates system,
Cross product
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