The geodesic equations describe the paths taken by particles moving under the influence of gravity in a curved spacetime, such as that described by Einstein's theory of general relativity. A geodesic represents the shortest path between two points in a curved space, analogous to a straight line in flat (Euclidean) space. In mathematical terms, the geodesic equations can be derived from the principle of least action or variational principles and are expressed in the form of a second-order differential equation.
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