- #1
member 731016
- Homework Statement
- Please see below
- Relevant Equations
- Please see below
For this problem,
My solution to (a) is,
We have constraint . There are many places we could define our (x,y) Cartesian coordinate system. However, the most easiest I think for the problem would be to attach a and coordinate system at the COM of . We define parallel to rightward horizontal and parallel to upwards vertical.
Since the COM of is not moving with respect to our defined coordinate system (orange dot denotes m_1 COM in diagram above), then we omit KE in the Lagrangian form of the system. The coordinates of is
The velocity coordinates are by definition the time with respect to the linear time (I think we could generalize this from being with respect to linear time to being with respect to any non-linear, higher dimensional time ). However, we assume classical case. Thus
Thus by definition of T and V, Lagrangian is
However, does anybody please know whether I am correct so far?
Thanks!
My solution to (a) is,
We have constraint
Since the COM of
The velocity coordinates are by definition the time with respect to the linear time
Thus by definition of T and V, Lagrangian is
However, does anybody please know whether I am correct so far?
Thanks!