- #1

cpsinkule

- 174

- 24

## Homework Statement

2 masses, m[itex]_{1}[/itex] and m[itex]_{2}[/itex] are fixed at the endpoints of a rigid rod of length l. mass m[itex]_{1}[/itex] is attached to a horizontal bar so that it may move in the x direction freely, but not in the y direction. let θ be the angle the rod makes with the vertical, what is the corresponding Lagrangian of the system if it is assumed to be in the uniform gravitational field g?

## Homework Equations

Euler Lagrange eqns

## The Attempt at a Solution

The only issue I am running into with this problem is in the kinetic energy terms. My kinetic terms are : [itex]\frac{1}{2}[/itex](m[itex]_{1}[/itex]+m[itex]_{2}[/itex])[itex]\dot{x}[/itex][itex]^{2}[/itex]+[itex]\frac{1}{2}[/itex]m[itex]_{2}[/itex]l[itex]^{2}[/itex][itex]\dot{θ}[/itex][itex]^{2}[/itex] but the book proposes a solution the same as mine except with the added term [itex]\frac{1}{2}[/itex]m[itex]_{2}[/itex](2l[itex]\dot{x}[/itex][itex]\dot{θ}[/itex]cosθ). I am not understanding where this term comes from, I thought I took care of the x velocity dependence in the first term.