Classical Dynamics of Particles and Systems
Classical Dynamics of Particles and Systems
5th Edition
ISBN: 9780534408961
Author: Stephen T. Thornton, Jerry B. Marion
Publisher: Cengage Learning
Question
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Chapter 1, Problem 1.1P
To determine

The transformation matrix for rotation about x2 axis.

Expert Solution & Answer
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Answer to Problem 1.1P

The transformation matrix for rotation about x2 axis is (1201201012012).

Explanation of Solution

Consider the rotation given in the below figure.

Classical Dynamics of Particles and Systems, Chapter 1, Problem 1.1P

Rotation matrix for rotation about x2 or y axis in 3-D is,

    Ry(θ)=(cosθ0sinθ010sinθ0cosθ)

Here, Ry(θ) is the transformation matrix and θ is the angle of rotation.

Conclusion:

Substitute 45° for θ to get Ry(θ).

    Ry(θ)=(cos45°0sin45°010sin45°0cos45°)=(1201201012012)

Therefore, transformation matrix for rotation about x2 axis is (1201201012012).

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