(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Prove that in parabolic coordinates [itex]\alpha,\beta[/itex] the kinetic energy is [itex]T=m/8(\alpha+\beta)(\dot\alpha^2/\alpha+\dot\beta^2/\beta)[/itex]

2. Relevant equations

Parabolic coordinates are defined as follows: [itex]\alpha=r+x, \beta=r-x[/itex] with [itex]r=\sqrt{x^2+y^2}[/itex]

3. The attempt at a solution

I don't know how to proceed in this situation: in simpler case (spherical or cylindrical coordinates) I write down the three components of velocity using geometrical intuition (e.g. [itex]v_\rho=\dot \rho, v_\phi=\rho \dot\phi,v_z=\dot z[/itex], because Iseethey are right...). What if I get only thedefinitionof the new coordinates?

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# Homework Help: Kinetic energy in parabolic coordinates

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