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NoPhysicsGenius

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My question pertains to Example 1.2 of Schaum's Outline of Lagrangian Dynamics by Dare A. Wells, chapter 1, page 4.

You can view the diagram and the example (1.2) by going to the following link on Amazon.com and clicking on Excerpt, and then going to page 4:

https://www.amazon.com/gp/product/0070692580/?tag=pfamazon01-20

The goal of the example is to take the equations of motion in the inertial coordinates and find the corresponding equations of motion in the noninertial coordinates.

I'm confused on the part that says, "Reference to the figure shows that":

[tex]x_1 = x_2 \cos \omega t - y_2 \sin \omega t[/tex]

[tex]y_1 = x_2 \sin \omega t + y_2 \cos \omega t[/tex]

I don't understand how these two expressions have been derived. Can someone please explain this to me?

Thank you.

You can view the diagram and the example (1.2) by going to the following link on Amazon.com and clicking on Excerpt, and then going to page 4:

https://www.amazon.com/gp/product/0070692580/?tag=pfamazon01-20

The goal of the example is to take the equations of motion in the inertial coordinates and find the corresponding equations of motion in the noninertial coordinates.

I'm confused on the part that says, "Reference to the figure shows that":

[tex]x_1 = x_2 \cos \omega t - y_2 \sin \omega t[/tex]

[tex]y_1 = x_2 \sin \omega t + y_2 \cos \omega t[/tex]

I don't understand how these two expressions have been derived. Can someone please explain this to me?

Thank you.

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