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Dor_M
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My question is from an exam in analytic mechanics. The question was about an object sliding on inclined plane, the plane's angle is constant, and the plane is free to move along X axis. No friction.
The problem is originaly three degrees of freedom, (x, y) of the object and (X) of the plane. The constant angle brings you to two degrees of freedom.
Now, I used the momentum conservation along the x-axis as a constrain, and got a lagrangian with one degree of freedom. I know it's not what was expected, and that they wanted me to get the conservation of the momentum along x from the lagrangian, but is it wrong? The constrain is holonomic for my understanding. Also I received the correct results.
another thing is that the second question was "which conservations do you have in the problem". I answered that the energy is conserved, my lagrangian didn't contained X anymore, but only a coordinate that describe the distance of the object from the edge of the plane, and it wasn't cyclic. I answered that the energy alone is conserved.
So,
1. Is it a mistake to use the momentum conservation as holonomic constraint in this case, and if it is, why? (even though I got the correct results)
2. If I got rid of X in the lagrangian, should I still count it's momentum as conserved?
(I'm sorry for spelling mistakes, english is not my first language.)
My question is from an exam in analytic mechanics. The question was about an object sliding on inclined plane, the plane's angle is constant, and the plane is free to move along X axis. No friction.
The problem is originaly three degrees of freedom, (x, y) of the object and (X) of the plane. The constant angle brings you to two degrees of freedom.
Now, I used the momentum conservation along the x-axis as a constrain, and got a lagrangian with one degree of freedom. I know it's not what was expected, and that they wanted me to get the conservation of the momentum along x from the lagrangian, but is it wrong? The constrain is holonomic for my understanding. Also I received the correct results.
another thing is that the second question was "which conservations do you have in the problem". I answered that the energy is conserved, my lagrangian didn't contained X anymore, but only a coordinate that describe the distance of the object from the edge of the plane, and it wasn't cyclic. I answered that the energy alone is conserved.
So,
1. Is it a mistake to use the momentum conservation as holonomic constraint in this case, and if it is, why? (even though I got the correct results)
2. If I got rid of X in the lagrangian, should I still count it's momentum as conserved?
(I'm sorry for spelling mistakes, english is not my first language.)
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