An object is moving between two points on a circle with radius R. The object can only move along the circle. The function F is the path length travelled between two points on the circle. a. Assume that the position of the object along the circle is described by an angle θ with respect to the center of the circle and the x-axis. Is this angle a minimum set of generalized coordinates for this problem? b. Assume that the position of the object along the circle is described by two Cartesian coordinates x and y, where the origin of the coordinate system is the center of the circle. Are these coordinates a minimum set of generalized coordinates for this problem? c. What would be the holonomic constraint for the two Cartesian coordinates x and y for the motion around the circle?
An object is moving between two points on a circle with radius R. The object can only move along the circle. The function F is the path length travelled between two points on the circle. a. Assume that the position of the object along the circle is described by an angle θ with respect to the center of the circle and the x-axis. Is this angle a minimum set of generalized coordinates for this problem? b. Assume that the position of the object along the circle is described by two Cartesian coordinates x and y, where the origin of the coordinate system is the center of the circle. Are these coordinates a minimum set of generalized coordinates for this problem? c. What would be the holonomic constraint for the two Cartesian coordinates x and y for the motion around the circle? d. What would be the Euler equation for this problem in Cartesian coordinates with holonomic constraint and Lagrange multiplier λ.
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