Page 133 - Dynamics of Mechanical Systems

0593_C04*_fm Page 114 Monday, May 6, 2002 2:06 PM

114 Dynamics of Mechanical Systems

Problems

Section 4.2 Orientation of Rigid Bodies
P4.2.1: In Eq. (4.2.3), suppose that the orientation angles are α = 30°, β = –45°, and γ = 60°.
Determine the transformation matrix S and verify that S is orthogonal; that is, the inverse
S is equal to the transpose.
–1

Section 4.3 Configuration Graphs

P4.3.1: Consider the configuration graph of Figure P4.3.1. Find the relations between the
N and the n . Express the results in the matrix forms:
i i

N = S n and n = T N
Show that:

ST = S −1
=
T
ˆ
ˆ
i N N n n
N
i i i i
1
2
3
FIGURE P4.3.1 θ θ θ
Configuration graph. 1 2 3

P4.3.2: Repeat Problem P4.3.1 for the configuration graph of Figure P4.3.2.

ˆ
i N N n ˆ n
N
i i i i
1
2

3
FIGURE P4.3.2 θ θ θ
Configuration graph. 1 2 3

Section 4.4 Simple Angular Velocity and Simple Angular Acceleration

P4.4.1: A flywheel rotating at 400 rpm is brought to rest in 3 minutes by a uniform braking
moment. Determine the angular deceleration and the number of revolutions turned
through during the braking.
P4.4.2: Consider the rotating disk D of Figure P4.4.2 where θ is the rotation angle of D.
Let AB be a line scribed on D, and let φ be the angle AB makes with a fixed horizontal