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  2. Equations of motion - Wikipedia

    en.wikipedia.org/wiki/Equations_of_motion

    A differential equation of motion, usually identified as some physical law (for example, F = ma) and applying definitions of physical quantities, is used to set up an equation for the problem. [ clarification needed ] Solving the differential equation will lead to a general solution with arbitrary constants, the arbitrariness corresponding to a ...

  3. Three-body problem - Wikipedia

    en.wikipedia.org/wiki/Three-body_problem

    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

  4. Newton's laws of motion - Wikipedia

    en.wikipedia.org/wiki/Newton's_laws_of_motion

    If a third mass is added, the Kepler problem becomes the three-body problem, which in general has no exact solution in closed form. That is, there is no way to start from the differential equations implied by Newton's laws and, after a finite sequence of standard mathematical operations, obtain equations that express the three bodies' motions ...

  5. n-body problem - Wikipedia

    en.wikipedia.org/wiki/N-body_problem

    The equation α + ⁠ η / r 3 ⁠ r = 0 is the fundamental differential equation for the two-body problem Bernoulli solved in 1734. Notice for this approach forces have to be determined first, then the equation of motion resolved. This differential equation has elliptic, or parabolic or hyperbolic solutions. [23] [24] [25]

  6. Relative velocity - Wikipedia

    en.wikipedia.org/wiki/Relative_velocity

    Relative velocities between two particles in classical mechanics. The figure shows two objects A and B moving at constant velocity. The equations of motion are: = +, = +, where the subscript i refers to the initial displacement (at time t equal to zero).

  7. Classical central-force problem - Wikipedia

    en.wikipedia.org/.../Classical_central-force_problem

    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.

  8. Euler's three-body problem - Wikipedia

    en.wikipedia.org/wiki/Euler's_three-body_problem

    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.

  9. Lagrangian mechanics - Wikipedia

    en.wikipedia.org/wiki/Lagrangian_mechanics

    Eliminating the angular velocity dθ/dt from this radial equation, [47] ¨ = +. which is the equation of motion for a one-dimensional problem in which a particle of mass μ is subjected to the inward central force −dV/dr and a second outward force, called in this context the (Lagrangian) centrifugal force (see centrifugal force#Other uses of ...