Geodesic deviation & Jacobi Equation

In summary, Geodesic deviation is the measure of how two geodesics on a curved surface diverge or converge. The Jacobi equation is a mathematical equation that describes this deviation and is used to calculate it over time. Factors such as the curvature of space, initial conditions, and external forces can affect geodesic deviation. It is important in the study of general relativity and has practical applications in navigation and satellite technology.
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They are the same notion under a different name: The Euler-Lagrange equations for the variation of geodesic length, over the space of geodesics with fixed ends.
 

FAQ: Geodesic deviation & Jacobi Equation

What is Geodesic deviation?

Geodesic deviation is the measure of how two geodesics (the shortest path between two points on a curved surface) diverge or converge.

What is the Jacobi Equation?

The Jacobi equation is a mathematical equation that describes the deviation of a geodesic from a reference geodesic in a curved space.

How is the Jacobi Equation related to Geodesic deviation?

The Jacobi equation is used to calculate the geodesic deviation, as it describes how the deviation of a geodesic changes over time.

What factors affect Geodesic deviation?

The factors that affect geodesic deviation include the curvature of the space, the initial conditions of the geodesics, and the presence of external forces.

Why is Geodesic deviation important?

Geodesic deviation is important in the study of general relativity, as it helps us understand the effects of gravity on the motion of objects in curved spacetimes. It is also used in navigation and satellite technology to calculate the most efficient paths between two points.

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