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An osculating circle is a circle that best approximates the curvature of a curve at a specific point. It is tangent to the curve at that point and has the same curvature as the curve at that point. [2] The osculating circle provides a way to understand the local behavior of a curve and is commonly used in differential geometry and calculus.
In mechanics and physics, simple harmonic motion (sometimes abbreviated as SHM) is a special type of periodic motion an object experiences by means of a restoring force whose magnitude is directly proportional to the distance of the object from an equilibrium position and acts towards the equilibrium position.
The Tusi couple (also known as Tusi's mechanism [1] [2] [3]) is a mathematical device in which a small circle rotates inside a larger circle twice the diameter of the smaller circle. Rotations of the circles cause a point on the circumference of the smaller circle to oscillate back and forth in linear motion along a diameter of the larger circle.
The energy of the system is oscillating back and forth between kinetic energy and potential energy. In the animation with the two circling masses there is a back and forth oscillation of kinetic energy and potential energy.
Animation showing curve adaptation as the ratio a / b increases from 0 to 1. The animation shows the curve adaptation with continuously increasing a / b fraction from 0 to 1 in steps of 0.01 (δ = 0). Below are examples of Lissajous figures with an odd natural number a, an even natural number b, and | a − b | = 1.
The osculating circle to C at p, the osculating curve from the family of circles. The osculating circle shares both its first and second derivatives (equivalently, its slope and curvature) with C. [1] [2] [4] The osculating parabola to C at p, the osculating curve from the family of parabolas, has third order contact with C. [2] [4]
The cam can be seen as a device that converts rotational motion to reciprocating (or sometimes oscillating) motion. [clarification needed] [3] A common example is the camshaft of an automobile, which takes the rotary motion of the engine and converts it into the reciprocating motion necessary to operate the intake and exhaust valves of the cylinders.
Animation depicting evolution of a Cornu spiral with the tangential circle with the same radius of curvature as at its tip, also known as an osculating circle.. To travel along a circular path, an object needs to be subject to a centripetal acceleration (for example: the Moon circles around the Earth because of gravity; a car turns its front wheels inward to generate a centripetal force).