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Lagrangian Mechanics: Find Lagrangian & Hamiltonian of Pendulum
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[QUOTE="Jezza, post: 5489740, member: 574693"] I would use polar coordinates with the origin at the fixing point and theta the angle between the spring and the vertical. That way you have orthogonal coordinates so you don't get cross-terms in the kinetic energy, and the potential energy of the spring is expressed easily in terms of r. V is just mgr(1-cos(theta)) then. If you define theta as the angle between the spring and the horizontal then the potential energy will be slightly neater, but then your equilibrium position will be at theta=pi/2 and that will only make life difficult if you want to find the frequency of small oscillations about the equilibrium. If you go ahead with your coordinates, you'll find a bit of algebra will get you to polar coordinates in the end, though as has been mentioned you need to reverse the sign in your elastic potential energy. I think the sign on your gravitational potential energy needs to be reversed too, but I'm unsure of exactly how you've defined your coordinates. Just remember the gravitational potential increases as the mass moves up! [/QUOTE]
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Lagrangian Mechanics: Find Lagrangian & Hamiltonian of Pendulum
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