Possible Error in Marion and Thornton's Classical Dynamics of Particles and Systems

Physics Asked by Elvis on November 29, 2020

so I was going over my notes on classical mechanics and just started to review rotation matrices which is the first topic the book starts with. On page 3

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The rotation matrix associated with 1.2a and 1.2b is

costheta & sintheta \
-sintheta & costheta \

but when I try to derive the matrix by following the unit vectors $hat i$ and $hat j$

I get

costheta & -sintheta \
sintheta & costheta \

The one that the book derives would be clockwise rotation, and the one I got would be for counter-clockwise rotation correct?

One Answer

You can construct the rotation matrix by finding the direction cosines defined as $lambda_{i,j}=cos(x'_{i},x_{j})$ so:





The book is right.

Answered by Alberto Navarro on November 29, 2020

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