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What are kinetic and geometric constraints?

  1. Jun 7, 2015 #1
    1. The problem statement, all variables and given/known data
    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 modelled 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.

    2. Relevant equations
    I have no idea what the relevant equations for this problem are. I think these equations may be relevant:
    • F=ma
    • Fcentripetal=mv2/r
    • v=rω

    3. 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 lenght L + extension x. So centripetal force can be written as Fcentripetal=mrω2 --> m(L+x)(dθ/dt)2. And I guess this is kinetic.
    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.
     
  2. jcsd
  3. Jun 7, 2015 #2
    I think you are working on Lagrangian mechanics so think about Lagrangian function of action.
     
  4. Jun 7, 2015 #3

    haruspex

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    I believe the "type (e.g. geometric, kinetic)" refers to constraints, not to forces. Certainly I would not describe mg as 'geometric'.
    It asks for "all forces and constraints that are applied". Centripetal force is not an applied force. I guess you could characterise it as a constraint.
    To see angle φ you need to look at the plan view, i.e. what does it look like from above? ##\dot\phi## would be the angular velocity about the vertical axis.
    That's the angular velocity about a horizontal axis perpendicular to the plane containing the pendulum 'sticks'.
    At any instant, both φ and θ may be changing, so the overall angular velocity is the vector sum of the two.
     
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