Where r is equal and y' is equal, then the absolute value of y "must be equal. At that point, the two curves have the same bending direction and the same sign, so the second derivative is equal.
According to the rotation rate of the tangent direction angle of a point on the curve to the arc length, it is defined by differentiation, which indicates the degree of deviation of the curve from the straight line. A numerical value that mathematically represents the degree of curvature of a curve at a certain point. The greater the curvature, the greater the curvature of the curve. The reciprocal of curvature is the radius of curvature.
Extended data:
Curvature circle and curve have the same tangent and curvature at m point; There is the same concave direction as the curve near point M, so in practical engineering design problems, a circular arc with a curvature circle near point M is often used to approximate the curve arc to simplify the problem.
In dynamics, generally speaking, when an object moves at variable speed relative to another object, it will also produce curvature. This is about the distortion of time and space. Combined with the equivalence principle of general relativity, an object with variable speed motion can be regarded as being in a gravitational field, resulting in curvature.
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