Curvature in polar coordinates

Thread starter mahdi200hell
Start date Oct 29, 2010
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Coordinates Curvature Polar Polar coordinates

In summary, curvature in polar coordinates is a measure of how much a curve deviates from being a straight line. It is determined by the distance from the origin and the angle between the tangent line and the radial line, and can be calculated using a specific formula. Curvature is significant in understanding the shape and behavior of curves in polar coordinates, and can change as the curve evolves depending on the rate of change of the distance from the origin.

Oct 29, 2010

mahdi200hell

hi
i need a affirm of curvature in polar coordinates.
i need now
please

Last edited: Oct 29, 2010

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Oct 29, 2010

Mark44

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mahdi200hell said:

hi
i need a affirm of curvature in polar coordinates.
i need now
please

What does this mean, you need an "affirm" of curvature?

Related to Curvature in polar coordinates

1. What is curvature in polar coordinates?

Curvature in polar coordinates is a measure of how much a curve deviates from being a straight line. It is calculated by finding the rate of change of the tangent angle along the curve.

2. How is curvature related to polar coordinates?

In polar coordinates, the curvature is determined by the distance from the origin and the angle between the tangent line and the radial line. This is different from Cartesian coordinates, where curvature is determined by the second derivative of the curve.

3. How is curvature calculated in polar coordinates?

The curvature in polar coordinates can be calculated using the formula:
κ = (r^2 + 2r'^2 - rr'') / (r^2 + r'^2)^(3/2)
where r is the distance from the origin and r' and r'' are the first and second derivatives of r with respect to the tangent angle.

4. What is the significance of curvature in polar coordinates?

Curvature in polar coordinates is important in understanding the shape and behavior of curves in polar coordinates. It can help determine the maximum and minimum points of a curve, as well as the direction in which the curve is turning.

5. How does curvature change as the curve evolves in polar coordinates?

The curvature of a curve in polar coordinates can change as the curve evolves. If the distance from the origin is constant, the curvature will only change with the change in the tangent angle. However, if the distance from the origin is changing, the curvature will also be affected by the rate of change of the distance from the origin.