Create successful ePaper yourself
Turn your PDF publications into a flip-book with our unique Google optimized e-Paper software.
14 Velocity and acceleration of rigid body 3D<br />
14.1 Using Vehicle dynamics notations<br />
F x<br />
Nasser M. Abbasi<br />
3d_1.vsd<br />
May 26, 2011<br />
L<br />
I <br />
N<br />
F z<br />
W<br />
z<br />
r<br />
Linear force<br />
torque<br />
Linear velocity<br />
angular velocity<br />
v <br />
y<br />
<br />
p q V<br />
x<br />
M<br />
F y<br />
U<br />
F <br />
Forces, Torques, linear<br />
velocities and angular velocities<br />
for a general 3D rigid body<br />
I xx I xy I xz<br />
<br />
I yx I yy I yz<br />
linear momentum<br />
U qW rV<br />
F d dt p d dt mvm d dt v m a<br />
V rU pW<br />
W pV qU<br />
U<br />
V<br />
W<br />
p<br />
q<br />
r<br />
F x<br />
F y<br />
F z<br />
L<br />
M<br />
N<br />
d dt H d dt I<br />
Angular momentum<br />
Derivation of this is much more complicated than with<br />
the case of linear motion (F=ma), since m is scalar<br />
there, but for rotation, I is matrix. See next page for the<br />
derivation<br />
58