We first build a simple roly-poly toy model and then consider the model with a person standing on it. т r mg N where,

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We first build a simple roly-poly toy model and then consider the model with a person standing on it. т r mg N
where, we further simplify the roly-poly toy on the xz plane, where point C is the center of gravity, 0 is the geometric center of the hemisphere, h is the distance between 0 and C, mg is the gravity of this hemisphere, A is the contacting point, r is the radius of the hemisphere, e is the variable to descirbe the movement of this hemisphere, the normal force and the friction from the ground to the hemisphere are respectively N and F.
where x is the x-coordinate of 0. Consider no slipping on the contact point, we also have: x = -Or. Then, we have: Ö= hmsino (g + r02) Ic + m(r2 + h2 - 2hrcose) (3) The above equation of motion can also be derived using Euler-Lagrange equation. (a) Please first use equation (3) and solve (t) ,'(t), h(t) and plot them. Then, make an animation describing the motion of this roly-polytoy. Here, he is the y-coordinate of C and we take these parameters: h = år, Is = mra, r = 0.5m, m = 250kg, e(t = 0) = 60°. 83 320