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**1. The problem statement, all variables and given/known data**

I am trying to find motion equations for a mass moving around a big mass (ex. planet around sun), assumption is that the mass in middle is static (so this can be reduced to moving of mass around central force in middle of cartesian system), and everything would be good but I dont know what to do with Coriolis effect (I am using polar system with angle and radius as generalised coordinates), using Hamilton mechanics

**2. Relevant equations**

Hamilton equations, differential equations, motion equations

**3. The attempt at a solution**

I have generalized coordinates in polar system: [tex]r,\phi,p_r,p_\phi[/tex] and I gonna find lagrangial and hamiltonian, depending on general definition of both functions

[tex]\mathcal{L}\left(r,\phi,\dot r,\dot\phi\right)=\frac{m}{2}\left(\dot r^2+r^2\dot\phi^2\right)-U(r)[/tex]

now I find potential of centrifugal and central force

[tex]\mathcal{L}\left(r,\phi,\dot r,\dot\phi\right)=\frac{m}{2}\left(\dot r^2+r^2\dot\phi^2\right)+\frac{GMm}{r}-\frac{\ell^2}{2mr^2}-U\left(F_c\right)[/tex]

and now my problem is, what to do with general potential of Coriolis force? I know I can write is similar to electromagnetic force potential, but I dont know if Coriolis effect exist in this kind of motion (this system is inertial and Coriolis effect is connected with not inertial systems), when I know this, it will not be a big problem to find hamilton equations and finish divagations, so I only need answer for this, with explanation please;] thank you!