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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 corresponding solutions for the orbits.
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 problem of two fixed centers conserves energy; in other words, the total energy is a constant of motion.The potential energy is given by =where represents the particle's position, and and are the distances between the particle and the centers of force; and are constants that measure the strength of the first and second forces, respectively.
The three-body problem is a special case of the n-body problem, which describes how n objects move under one of the physical forces, such as gravity. These problems have a global analytical solution in the form of a convergent power series, as was proven by Karl F. Sundman for n = 3 and by Qiudong Wang for n > 3 (see n -body problem for details).
In theoretical physics, the hierarchy problem is the problem concerning the large discrepancy between aspects of the weak force and gravity. [1] There is no scientific consensus on why, for example, the weak force is 10 24 times stronger than gravity .
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.
Classical mechanics is the branch of physics used to describe the motion of macroscopic objects. [1] It is the most familiar of the theories of physics. The concepts it covers, such as mass, acceleration, and force, are commonly used and known. [2] The subject is based upon a three-dimensional Euclidean space with fixed axes, called a frame of ...
The block-stacking problem is the following puzzle: Place N {\displaystyle N} identical rigid rectangular blocks in a stable stack on a table edge in such a way as to maximize the overhang. Paterson et al. (2007) provide a long list of references on this problem going back to mechanics texts from the middle of the 19th century.