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Exact solutions of classical central-force problems. In the classical central-force problem of classical mechanics, some potential energy functions produce motions or orbits that can be expressed in terms of well-known functions, such as the trigonometric functions and elliptic functions. This article describes these functions and the ...
Kepler problem. In classical mechanics, the Kepler problem is a special case of the two-body problem, in which the two bodies interact by a central force that varies in strength as the inverse square of the distance between them. The force may be either attractive or repulsive. The problem is to find the position or speed of the two bodies over ...
t. e. In classical mechanics, the central-force problem is to determine the motion of a particle in a single central potential field. A central force is a force (possibly negative) that points from the particle directly towards a fixed point in space, the center, and whose magnitude only depends on the distance of the object to the center.
The Binet equation, derived by Jacques Philippe Marie Binet, provides the form of a central force given the shape of the orbital motion in plane polar coordinates. The equation can also be used to derive the shape of the orbit for a given force law, but this usually involves the solution to a second order nonlinear, ordinary differential equation.
The capstan equation[1] or belt friction equation, also known as Euler–Eytelwein formula[2] (after Leonhard Euler and Johann Albert Eytelwein), [3] relates the hold-force to the load-force if a flexible line is wound around a cylinder (a bollard, a winch or a capstan). [4][1] It also applies for fractions of one turn as occur with rope drives ...
The general equation can then be written as [6] = + + (),. where the "force" term corresponds to the forces exerted on the particles by an external influence (not by the particles themselves), the "diff" term represents the diffusion of particles, and "coll" is the collision term – accounting for the forces acting between particles in collisions.
Differential equations. In mathematics, the power series method is used to seek a power series solution to certain differential equations. In general, such a solution assumes a power series with unknown coefficients, then substitutes that solution into the differential equation to find a recurrence relation for the coefficients.
Power is the amount of energy transferred or converted per unit time. In the International System of Units, the unit of power is the watt, equal to one joule per second. Power is a scalar quantity. Specifying power in particular systems may require attention to other quantities; for example, the power involved in moving a ground vehicle is the ...