Problem 3 A ball of mass m, slides over a sliding inclined plane of mass M and angle a. Denote by X. the cordinate of O' with re spect to 0, and by (xy) the coordinate of m with respoct to O'(e figure below) 1. Calculate the degrwe of freedom of the system 2. Find the velocity of m with nespect to 0. 3. Write the expnossion of the Lagrangian function 4. Derive the Euler Lagrange equations 5. Find z" and X" in terms of the masses (m,M), angle a and
Problem 3 A ball of mass m, slides over a sliding inclined plane of mass M and angle a. Denote by X. the cordinate of O' with re spect to 0, and by (xy) the coordinate of m with respoct to O'(e figure below) 1. Calculate the degrwe of freedom of the system 2. Find the velocity of m with nespect to 0. 3. Write the expnossion of the Lagrangian function 4. Derive the Euler Lagrange equations 5. Find z" and X" in terms of the masses (m,M), angle a and
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Transcribed Image Text:Problem 3
A ball of mass m, slides over a
sliding inclined plane of mas
M and angle a. Denote by X,
the cocrdinate of O' with re
spect to 0, and by (xy) the
coordinate of m with nespoct
to O'(see figure below)
m
M.
O'
1. Caleulate the degree of freedom of the system
2. Find the velocity of m with respect to o.
3. Write the exprossion of the Lagrangi an functian
4. Derive the Euler Lagrange equations
5. Find z" and X" in terms of the masses (m,M), angle a and g
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