CLASSICAL DYNAMICS OF PARTICLES AND SYST
CLASSICAL DYNAMICS OF PARTICLES AND SYST
5th Edition
ISBN: 9780357670675
Author: Thornton
Publisher: CENGAGE L
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 SYST, 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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