- #1
tanaygupta2000
- 208
- 14
- Homework Statement
- A particle of mass 'm' is tied to one end of a massless spring (spring constant k and unstretched length r0). The other end of the spring is fixed to a point P on a smooth horizontal plane on which this particle is moving. If the instantaneous position of this particle is (r,θ), then obtain the Lagrangian and Hamiltonian of the ststem. Also find equations of motion of the system.
- Relevant Equations
- Lagrangian, L = KE - PE
Hamiltonian, H = Σpx(dot) - L
Euler Lagrange equation, ∂L/∂q - d/dt (∂L/∂q(dot)) = 0
I know that from the given problem, I need to find the expression for Kinetic energy,
KE = 1/2 m [r(dot)]^2
and Potential energy,
PE = 1/2 k r^2
So L = 1/2 m [r(dot)]^2 - 1/2 k r^2
Hence H = 1/2 m [r(dot)]^2 + 1/2 k r^2
I assume that the fixed length r0 is provided to find the value of end constants.
But what is the function of theta? Is it a generalized coordinate ?
KE = 1/2 m [r(dot)]^2
and Potential energy,
PE = 1/2 k r^2
So L = 1/2 m [r(dot)]^2 - 1/2 k r^2
Hence H = 1/2 m [r(dot)]^2 + 1/2 k r^2
I assume that the fixed length r0 is provided to find the value of end constants.
But what is the function of theta? Is it a generalized coordinate ?