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No_Tumbleweed_8157 t1_j6lqkou wrote

Maybe the first few weeks of Classical Mechanics?

The bulk of my classical mechanics course was spent on nonstandard analysis, gravitational integral problems, and brain-melting rotational inertia tensor calculations.

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Shamon_Yu OP t1_j6lrlrc wrote

But applied to academic problems involving point masses, linear springs, and inifinitely rigid bodies :)

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No_Tumbleweed_8157 t1_j6na77z wrote

Interesting. Do Engineers study Lagrange equations and the double pendulum?

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Shamon_Yu OP t1_j6nehd0 wrote

Kind of. Calculus of variations is typical in structural mechanics, but Lagrange equations specifically are not that important. Double pendulum is perhaps introduced, but not studied really.

My point was mainly that engineers have PDEs and physicists have ODEs in classical mechanics.

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No_Tumbleweed_8157 t1_j6nmpck wrote

I guess it’s fair to say that Physicists will try to solve a PDE in cartesian space by parameterizing and reducing to an ODE in polar space where r could be constant.

I know Engineers are also usually happy to solve a problem graphically or by implicit forms. There are also times where engineers will just use one term of the small angle approximation and preemptively set bounds on the radius of convergence to θ<10°. (That’s fair, because an out of bounds θ means a bending modulus has already passed a buckling limit and the system is borked)

I don’t think it’s fair to say Physics student Classical Dynamics doesn’t use PDEs, though, especially since checking Lagrangian invariance of solutions only works for PDEs.

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