A disk of mass M and radius R rolls without slipping down a fixed inclined plane that makes an angle a with the horizontal plane. (see figure). RP) P.E = 0 (a) Write down the constraint equations and determine the number of degrees of freedom s. (b) Choose a convenient generalized coordinate. (c) Write down an expression for the Lagrangian of rolling ball. Given: the moment of inertia of the ball about its center is I, = }MR² (d) Calculate the generalized momenta.
A disk of mass M and radius R rolls without slipping down a fixed inclined plane that makes an angle a with the horizontal plane. (see figure). RP) P.E = 0 (a) Write down the constraint equations and determine the number of degrees of freedom s. (b) Choose a convenient generalized coordinate. (c) Write down an expression for the Lagrangian of rolling ball. Given: the moment of inertia of the ball about its center is I, = }MR² (d) Calculate the generalized momenta.
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Transcribed Image Text:A disk of mass M and radius R rolls without slipping down a fixed inclined plane
that makes an angle a with the horizontal plane. (see figure).
RPO
P.E = 0
(a) Write down the constraint equations and determine the number of degrees of
freedom s.
(b) Choose a convenient generalized coordinate.
(c) Write down an expression for the Lagrangian of rolling ball. Given: the
moment of inertia of the ball about its center is I, = }MR²
(d) Calculate the generalized momenta.
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