Particle dynamics on a cosine path.

AI Thread Summary
The discussion revolves around deriving the equations of motion for a particle traveling along a cosine path influenced by friction and gravity. The user has calculated the motion equations in a moving coordinate system but seeks assistance in relating these to the inertial system coordinates x1 and x2. The motion is compared to a pendulum bob, which also follows a cosine function but experiences damped harmonic motion due to friction. The problem is identified as a classic differential equation challenge. Assistance is requested to bridge the calculations between the two coordinate systems.
gilgtc
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Hello, I have attached the problem that I am referring to.

Basically I have a particle traveling on a path defined by a cosine function and I want the equations of motion with respect to the inertial system, if the particle is under the influence of friction and gravity.

I have calculated the equation of motion with respect to the moving coordinate system s but I am not sure how to relate that to x1 and x2 (the inertial system) which is what I ultimately need.

Your help is very much appreciated.

Thank you,

gilgtc
 

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The bob of a pendulum started from height "h" will exhibit motion defined by a cosine function. Because of friction in the piviot the pendulum will not oscillate indefinitely rather it will exhibit damped harmonic motion. I believe this is a classic Differential equation problem.
 
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