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copied!<p>Numerical integration of Newton's laws of motion would be what I'd recommend. Draw the free body diagram of the disk, give the initial conditions for the system, and numerically integrate the equations for acceleration and velocity forward in time. You have three degrees of freedom: x, y translation in the plane and the rotation perpendicular to the plane. So you'll have six simultaneous ODEs to solve: rates of change of linear and angular velocities, rates of change for two positions, and the rate of change of angular rotation.</p> <p>Be warned: friction and contact make that boundary condition between the disk and the table non-linear. It's not a trivial problem.</p> <p>There could be some simplifications by treating the disk as a point mass. I'd recommend looking at Kane's <a href="http://rads.stackoverflow.com/amzn/click/0070378460" rel="nofollow noreferrer">Dynamics</a> for a good understanding of the physics and how to best formulate the problem.</p> <p>I'm wondering if the bending of the path that you're imagining would occur with a perfectly balanced disk. I haven't worked it out, so I'm not certain. But if you took a perfectly balanced disk and spun it about its center there'd be no translation without an imbalance, because there's no net force to cause it to translate. Adding in an initial velocity in a given direction wouldn't change that.</p> <p>But it's easy to see a force that would cause the disk to deviate from the straight path if there was an imbalance in the disk. If I'm correct, you'll have to add an imbalance to your disk to see bending from a straight line. Perhaps someone who's a better physicist than me could weigh in.</p>

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