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A set of equations describing the trajectories of objects subject to a constant gravitational force under normal Earth-bound conditions.Assuming constant acceleration g due to Earth's gravity, Newton's law of universal gravitation simplifies to F = mg, where F is the force exerted on a mass m by the Earth's gravitational field of strength g.
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 the absence of a net external force, the center of mass moves at a constant speed in a straight line. This applies, for example, to a collision between two bodies. [52] If the total external force is not zero, then the center of mass changes velocity as though it were a point body of mass . This follows from the fact that the internal forces ...
Inverse dynamics is an inverse problem.It commonly refers to either inverse rigid body dynamics or inverse structural dynamics.Inverse rigid-body dynamics is a method for computing forces and/or moments of force (torques) based on the kinematics (motion) of a body and the body's inertial properties (mass and moment of inertia).
Dividing both force equations by the respective masses, subtracting the second equation from the first, and rearranging gives the equation ¨ = ¨ ¨ = = (+) where we have again used Newton's third law F 12 = −F 21 and where r is the displacement vector from mass 2 to mass 1, as defined above. The force between the two objects, which ...
where b is the force acting on the body per unit mass (dimensions of acceleration, misleadingly called the "body force"), and dm = ρ dV is an infinitesimal mass element of the body. Body forces and contact forces acting on the body lead to corresponding moments of those forces relative to a given point. Thus, the total applied torque M about ...
There are two main descriptions of motion: dynamics and kinematics.Dynamics is general, since the momenta, forces and energy of the particles are taken into account. In this instance, sometimes the term dynamics refers to the differential equations that the system satisfies (e.g., Newton's second law or Euler–Lagrange equations), and sometimes to the solutions to those equations.
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.