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Terilien
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Can someone explain how to derive the formula for geodesic deviation? i didn't quite understand it. I'm using schtuz's book.
The derivation I placed on my web page atTerilien said:Can someone explain how to derive the formula for geodesic deviation? i didn't quite understand it. I'm using schtuz's book.
Geodesic Deviation is a concept in differential geometry that describes the change in the distance between two points along a geodesic (a straight line on a curved surface) due to the curvature of the surface.
The formula for Geodesic Deviation can be derived using the concept of parallel transport, which involves moving a vector along a geodesic while maintaining its direction. This is done with the help of Christoffel symbols, which represent the curvature of the surface.
The formula for Geodesic Deviation was derived by the German mathematician and physicist, Hermann Schutz, in his book "Geometrical Methods of Mathematical Physics". He used the concept of parallel transport and the equations of motion to derive the formula.
Geodesic Deviation is an important concept in the study of general relativity, as it helps us understand the effects of gravity on the motion of objects in space. It is also used in navigation and geodesy to determine the shortest distance between two points on a curved surface.
Geodesic Deviation has various applications in fields such as astronomy, physics, and engineering. It is used to calculate the trajectory of space probes, to predict the motion of celestial bodies, and to design structures that can withstand gravitational forces. It is also used in the study of black holes and other phenomena related to gravity.