PHYS 3210 Midterm: PHYS 321 UVA PFNsol
Document Summary
Phys 321 solutions to practice final (december 2002): two masses, m and 2m are connected by a spring of constant k, leading to the po- tential. 2: what is the lagrangian for this system? (assume 3-dimensional motion. , find the equations of motion and the constants of the motion, show that a circular orbit about the point r. 3 is stable with re- spect to small perturbations. )2: the equations of motion are r dv. If we add the two equations we find that the total momentum. Hence the point (center of mass) can be taken fixed if we de- constant r. Transforming to spherical polar coordinates we have effl m r. The con- stants of motion are therefore the total energy, 3 m r dr dt and the orbital angular momentum l. 0 =: in a circular orbit we have r. 2 (we can choose, if we wish, mr. 2 we see that the effective potential has a minimum at.
