Consider the problem of three bodies two of which having mass M, one of them having mass m. Body m is in the middle between the other two, coupled to them by two equal linear springs in rest. Now fix the two bodies M and move body m for a small amount perpendicular to the connection line. Now...
Please consider a homogenous, but not constant field, for example given by mgh2.
Two bodies connected by a rigid rod falling free will start rotating when the field mgh2 is suddenly switched on, except they are at the same height at this moment.
I guess this case can be calculated easily...
Sorry for any confusion, but I am dedicatedly interested in the non-mgh case (where separation cannot be performed): I wonder under which circumstances there can be a closed solution nevertheless.
Hello Petr,
thanks, but I am not quite sure how to understand your answer. You distinguish four cases:
In the case the two masses form a rigid body, conservation of angular momentum says they rotate at all times the way they rotate at the beginning.
In the case of a central potential...
I wonder about the general solvability of the problem of two point masses, interacting via a central force, exposed to an external field.
Some special cases seem easy:
- interaction by a rigid rod
- any interaction, but the field and interaction forces "decoupled" (example: two...