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A ball of mass m, slides over a ey sliding inclined plane of mass M and angle a. Denote by X, the coordinate of O' with re- spect to 0, and by (x.y) the Coordinate of m with respect to O'(see figure below) M O' 1. Calculate the degree of freedom of the system 2. Find the velocity of m with respect to 0. 3. Write the expression of the Lagrangian function

A ball of mass m, slides over a ey sliding inclined plane of mass M and angle a. Denote by X, the coordinate of O' with re- spect to 0, and by (x.y) the Coordinate of m with respect to O'(see figure below) M O' 1. Calculate the degree of freedom of the system 2. Find the velocity of m with respect to 0. 3. Write the expression of the Lagrangian function

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Problem 3 A ball of mass m, slides over a ey sliding inclined plane of mass M and angle a. Denote by X, the coordinate of O' with re- spect to 0, and by (x.y) the Coordinate of m with respect 1. a O' to O'(see figure below) 1. Calculate the degree of freedom of the system 2. Find the velocity of m with respect to O. 3. Write the expression of the Lagrangian function 4. Derive the Euler Lagrange equations 5. Find r" and X" in terms of the masses (m.M), angle a and g
Transcribed Image Text:Problem 3 A ball of mass m, slides over a ey sliding inclined plane of mass M and angle a. Denote by X, the coordinate of O' with re- spect to 0, and by (x.y) the Coordinate of m with respect 1. a O' to O'(see figure below) 1. Calculate the degree of freedom of the system 2. Find the velocity of m with respect to O. 3. Write the expression of the Lagrangian function 4. Derive the Euler Lagrange equations 5. Find r" and X" in terms of the masses (m.M), angle a and g
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