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A good exercise is to solve the motion on an inclined plane at angle ##\theta##. The usual way by looking at tangential motion. Then, convert back to Cartesian coordinates.Atomillo said:
Equations of motion of a point sliding on a line of arbitrary shape
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The discussion centers on deriving the equations of motion for a point sliding along a non-linear path defined by a function f(x). The initial approach used conservation of energy to find velocity as a function of position, leading to confusion when trying to express velocity as a function of time. Participants clarify that motion in two dimensions requires considering both x and y components, which complicates the conversion from v(x) to v(t). The need for a more sophisticated method, such as the calculus of variations or the Brachistochrone problem, is suggested for accurately modeling the motion. The thread emphasizes the importance of correctly accounting for the relationship between the two dimensions to avoid misinterpretation of the results.
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