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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F73b745fb-3e47-45ba-976e-65083418eda2%2F2a8ec1ea-f4b1-4982-bb94-10b91daf1b44%2Faca36br_processed.jpeg&w=3840&q=75)
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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