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The general equation can then be written as [6] = + + (),. where the "force" term corresponds to the forces exerted on the particles by an external influence (not by the particles themselves), the "diff" term represents the diffusion of particles, and "coll" is the collision term – accounting for the forces acting between particles in collisions.
In physics, particularly in mechanics, specific kinetic energy is a fundamental concept that refers to the kinetic energy per unit mass of a body or system of bodies in motion. The specific kinetic energy of a system is a crucial parameter in understanding its dynamic behavior and plays a key role in various scientific and engineering applications.
The Penrose criterion in Plasma Physics is a criterion for the kinetic stability of a plasma with a given velocity-space distribution function. This criterion can be used to determine that all so-called "single-humped" distributions (those with a single maximum), are kinetically stable. It is not employed in accounting for the electric field.
In mathematics, stability theory addresses the stability of solutions of differential equations and of trajectories of dynamical systems under small perturbations of initial conditions. The heat equation , for example, is a stable partial differential equation because small perturbations of initial data lead to small variations in temperature ...
In three spatial dimensions, this is a system of three coupled second-order ordinary differential equations to solve, since there are three components in this vector equation. The solution is the position vector r of the particle at time t , subject to the initial conditions of r and v when t = 0.
The kinetic energy constrains to lie on an ellipsoid, whereas the angular momentum constraint constrains to lie on a sphere. These two surfaces intersect in two curves shaped like the edge of a taco that define the possible solutions for L {\displaystyle \mathbf {L} } .
In classical mechanics, Euler's rotation equations are a vectorial quasilinear first-order ordinary differential equation describing the rotation of a rigid body, using a rotating reference frame with angular velocity ω whose axes are fixed to the body. They are named in honour of Leonhard Euler.
The equation is used primarily in Statistical mechanics and Particle physics to model plasma. As such, it has been used to model and study Plasma in thermonuclear reactors. [4] [5] [6] It has also seen use in modeling of Active matter. [7] The equation and its properties have been studied in depth by Alexander Bobylev. [8]