카이스트 고전역학 족보 고전역학2 final solution

2015 Classical Mechanics II Final Exam
2015. 12. 18 13:00 ~ 19:00 (6 hours)

1. (a) A rigid body consisting of particles of mass is rotating about an axis through the origin with angular velocity . Show that the total kinetic energy is given as (4 points)
(b) Show that the angular momentum is written by (4 points)
(c) Show that, when is the moment of inertia tensor, (3 points)
If we write in matrix form, .
(d) Show that, when is the moment of inertia about the th principal axis and is the angular speed about the axis, (4 points)

Where is the transformation matrix to diagonalize the moment of inertia,


2. The Euler angles are defined as illustrated in the figure below.

(a) Show that the transformation from the system to the system is given as (4 points)
The first rotation is counterclockwise (CCW) through an angle about the -axis (figure (a)) and transform the system into the system as

The second rotation is counterclockwise (CCW) through…