- #1

freutel

- 11

- 0

## Homework Statement

The question is to specify all forces and constraints that are applied in a system of a two-seat merry go round model in terms of the generalised coordinates - and their type (e.g. geometric, kinetic).

http://i.imgur.com/FQ7PJyg.png

The system is modeled as central vertical rotation axis, with two identical pendulum-sticks attached to its top. Each pendulum is a (weightless) elastic stick of length L with a point-mass mattached to its end. The elastic sticks have a spring constant K [N/m]. The sticks are free to rotate horizontally around the central vertical axis (described by an angle φ), and can also move relative to the central vertical pole (indicated by angle θ in below Figure). The generalised coordinates are the two angles θ and φ [in radians] and extension x [in meters] of both sticks.

## Homework Equations

I have no idea what the relevant equations for this problem are. I think these equations may be relevant:

- F=ma
- F
_{centripetal}=mv^{2}/r - v=rω

## The Attempt at a Solution

So first to specify all the forces there is the gravitational force of the point masses which is always

*mg.*I guess this is geometric. Than you have the centripetal force. The angular velocity is de time derivative of angle θ and the radius is length L + extension x. So centripetal force can be written as

*F*-->

_{centripetal}=mrω^{2}*m(L+x)(dθ/dt)*. And I guess this is kinetic.

^{2}This is about everything I can come up with for this question but there are still some unanswered things. What is a constraint (both geometric and kinetic) and what does angle φ stand for? The reason I ask what angle φ stands for is because I don't get the description "The sticks are free to rotate horizontally around the central vertical axis (described by an angle φ)". The picture doesn't show an angle φ so that's why I am confused. A little help would be appreciated.