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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 ...
List of unsolved problems in physics. The following is a list of notable unsolved problems grouped into broad areas of physics. [1] Some of the major unsolved problems in physics are theoretical, meaning that existing theories seem incapable of explaining a certain observed phenomenon or experimental result. The others are experimental, meaning ...
In physics and astronomy, Euler's three-body problem is to solve for the motion of a particle that is acted upon by the gravitational field of two other point masses that are fixed in space. This problem is exactly solvable, and yields an approximate solution for particles moving in the gravitational fields of prolate and oblate spheroids.
For such problems, to achieve given accuracy, it takes much less computational time to use an implicit method with larger time steps, even taking into account that one needs to solve an equation of the form (1) at each time step. That said, whether one should use an explicit or implicit method depends upon the problem to be solved.
By contrast, subtracting equation (2) from equation (1) results in an equation that describes how the vector r = x 1 − x 2 between the masses changes with time. The solutions of these independent one-body problems can be combined to obtain the solutions for the trajectories x 1 (t) and x 2 (t). Center of mass motion (1st one-body problem)
Helmholtz equation. In mathematics, the Helmholtz equation is the eigenvalue problem for the Laplace operator. It corresponds to the linear partial differential equation : where ∇2 is the Laplace operator, k2 is the eigenvalue, and f is the (eigen)function. When the equation is applied to waves, k is known as the wave number.
Solving the equations It is important to realize that the Einstein field equations alone are not enough to determine the evolution of a gravitational system in many cases. They depend on the stress–energy tensor , which depends on the dynamics of matter and energy (such as trajectories of moving particles), which in turn depends on the ...
Poisson's equation. Siméon Denis Poisson. Poisson's equation is an elliptic partial differential equation of broad utility in theoretical physics. For example, the solution to Poisson's equation is the potential field caused by a given electric charge or mass density distribution; with the potential field known, one can then calculate ...
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