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A general momentum equation is obtained when the conservation relation is applied to momentum. When the intensive property φ is considered as the mass flux (also momentum density), that is, the product of mass density and flow velocity ρu, by substitution into the general continuity equation:
Even if q i is a Cartesian coordinate, p i will not be the same as the mechanical momentum if the potential depends on velocity. [6] Some sources represent the kinematic momentum by the symbol Π. [22] In this mathematical framework, a generalized momentum is associated with the generalized coordinates. Its components are defined as
Download as PDF; Printable version; In other projects Wikidata item ... Pages in category "Polysemy" The following 8 pages are in this category, out of 8 total. This ...
If the body is at rest (v = 0), i.e. in its center-of-momentum frame (p = 0), we have E = E 0 and m = m 0; thus the energy–momentum relation and both forms of the mass–energy relation (mentioned above) all become the same. A more general form of relation holds for general relativity.
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.
At time t, let a mass m travel at a velocity v, meaning the initial momentum of the system is p 1 = m v {\displaystyle \mathbf {p} _{\mathrm {1} }=m\mathbf {v} } Assuming u to be the velocity of the ablated mass d m with respect to the ground, at a time t + d t the momentum of the system becomes
Calculating the Minkowski norm squared of the four-momentum gives a Lorentz invariant quantity equal (up to factors of the speed of light c) to the square of the particle's proper mass: = = = + | | = where = is the metric tensor of special relativity with metric signature for definiteness chosen to be (–1, 1, 1, 1).
Polysemy is distinct from monosemy, where a word has a single meaning. [3] Polysemy is distinct from homonymy—or homophony—which is an accidental similarity between two or more words (such as bear the animal, and the verb bear); whereas homonymy is a mere linguistic coincidence, polysemy is not. In discerning whether a given set of meanings ...