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0593_C11_fm Page 379 Monday, May 6, 2002 2:59 PM

Generalized Dynamics: Kinematics and Kinetics 379

P (m )
2
2
B
P (m )
3
3
P (m )
1 1
G
P (m )
i i
P (m )
N
N
FIGURE 11.9.3
A rigid body B, modeled as a set R
of particles, moving in an inertial
reference frame R.
G
where M is the mass of B, I is the central inertia dyadic of B, a is the acceleration of G
in R, and ωω ωω and αα αα are the angular velocity and angular acceleration of B in R. Then, by
following the procedures of Section 11.5 leading to Eq. (11.5.7), we can express the gen-
eralized inertia forces on B as:
*
F = v G ⋅F * + ωω ⋅T * ( r = 1 ,… n , ) (11.9.6)
r q r ˙ q r ˙
As noted earlier, inertia forces are sometimes called passive forces. In this context, applied
forces (such as gravity and contact forces) are sometimes called active forces; hence, the
generalized forces of the foregoing section are often called generalized active forces.

11.10 Examples

We can illustrate the concept of generalized inertia forces with a few elementary examples.

Example 11.10.1: A Simple Pendulum
Consider first the simple pendulum of Figure 11.10.1. Recall that the pendulum bob P
moves in a circle with radius and that the velocity and acceleration of P in an inertial
reference frame R may be expressed as:

v = lθ ˙ n θ (11.10.1)
P

R O

n
θ θ

n
r
FIGURE 11.10.1
The simple pendulum. P