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In physics and engineering, a free body diagram (FBD; also called a force diagram) [1] is a graphical illustration used to visualize the applied forces, moments, and resulting reactions on a free body in a given condition. It depicts a body or connected bodies with all the applied forces and moments, and reactions, which act on the body(ies).
Free body diagram of a statically indeterminate beam In the beam construction on the right, the four unknown reactions are V A , V B , V C , and H A . The equilibrium equations are: [ 2 ]
The three-body problem is a special case of the n-body problem. Historically, the first specific three-body problem to receive extended study was the one involving the Earth, the Moon, and the Sun. [2] In an extended modern sense, a three-body problem is any problem in classical mechanics or quantum mechanics that models the motion of three ...
The two-body problem is interesting in astronomy because pairs of astronomical objects are often moving rapidly in arbitrary directions (so their motions become interesting), widely separated from one another (so they will not collide) and even more widely separated from other objects (so outside influences will be small enough to be ignored safely).
Jean d'Alembert (1717–1783). D'Alembert's principle, also known as the Lagrange–d'Alembert principle, is a statement of the fundamental classical laws of motion. It is named after its discoverer, the French physicist and mathematician Jean le Rond d'Alembert, and Italian-French mathematician Joseph Louis Lagrange.
Free body diagram of a body on which only gravity and air resistance act. The free body diagram on the right is for a projectile that experiences air resistance and the effects of gravity. Here, air resistance is assumed to be in the direction opposite of the projectile's velocity: F a i r = − f ( v ) ⋅ v ^ {\displaystyle \mathbf {F ...
The Euler three-body problem is known by a variety of names, such as the problem of two fixed centers, the Euler–Jacobi problem, and the two-center Kepler problem. The exact solution, in the full three dimensional case, can be expressed in terms of Weierstrass's elliptic functions [ 2 ] For convenience, the problem may also be solved by ...
A free body diagram is constructed and the relevant relationships of force and velocity are formulated using techniques from continuum mechanics. The variables which describe the system are: The variables which describe the system are: