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Conservation of momentum is a mathematical consequence of the homogeneity (shift symmetry) of space (position in space is the canonical conjugate quantity to momentum). That is, conservation of momentum is a consequence of the fact that the laws of physics do not depend on position; this is a special case of Noether's theorem. [25] For systems ...
A local conservation law is usually expressed mathematically as a continuity equation, a partial differential equation which gives a relation between the amount of the quantity and the "transport" of that quantity. It states that the amount of the conserved quantity at a point or within a volume can only change by the amount of the quantity ...
A form of Newton's second law, that force is the rate of change of momentum, also holds, as does the conservation of momentum. However, the definition of momentum is modified. Among the consequences of this is the fact that the more quickly a body moves, the harder it is to accelerate, and so, no matter how much force is applied, a body cannot ...
This equation also generalizes the advection equation. Other equations in physics, such as Gauss's law of the electric field and Gauss's law for gravity, have a similar mathematical form to the continuity equation, but are not usually referred to by the term "continuity equation", because j in those cases does not represent the flow of a real ...
The global versions can be united into a single global conservation law: the conservation of the energy-momentum 4-vector. The local versions of energy and momentum conservation (at any point in space-time) can also be united, into the conservation of a quantity defined locally at the space-time point: the stress–energy tensor [ 11 ] : 592 ...
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A continuity equation: Representing the conservation of mass. Conservation of momentum : Consisting of a form of the Navier–Stokes equations that describe hydrodynamical flow on the surface of a sphere under the assumption that vertical motion is much smaller than horizontal motion (hydrostasis) and that the fluid layer depth is small ...
Hamilton's equations give the time evolution of coordinates and conjugate momenta in four first-order differential equations, ˙ = ˙ = ˙ = ˙ = Momentum , which corresponds to the vertical component of angular momentum = ˙ , is a constant of motion. That is a consequence of the rotational symmetry of the ...