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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.
meter (m) distance: meter (m) direction: unitless impact parameter meter (m) differential (e.g. ) varied depending on context differential vector element of surface area A, with infinitesimally small magnitude and direction normal to surface S: square meter (m 2)
The most common description of the electromagnetic field uses two three-dimensional vector fields called the electric field and the magnetic field.These vector fields each have a value defined at every point of space and time and are thus often regarded as functions of the space and time coordinates.
The two dots on top of the x position vectors denote their second derivative with respect to time, or their acceleration vectors. Adding and subtracting these two equations decouples them into two one-body problems, which can be solved independently. Adding equations (1) and results in an equation describing the center of mass motion.
The dotted line is from the factor e ik·r. The light circles represent atoms. In condensed matter physics, Bloch's theorem states that solutions to the Schrödinger equation in a periodic potential can be expressed as plane waves modulated by periodic functions.
Thus, the motion still lies in a plane perpendicular to L and the magnitude A is conserved, from the equation A 2 = m 2 k 2 + 2mEL 2. The perturbation potential h ( r ) may be any sort of function, but should be significantly weaker than the main inverse-square force between the two bodies.
Maxwell's equations seem overdetermined, in that they involve six unknowns (the three components of E and B) but eight equations (one for each of the two Gauss's laws, three vector components each for Faraday's and Ampère's circuital laws).
The multipole expansion circumvents this difficulty by expanding not E or B, but r ⋅ E or r ⋅ B into spherical harmonics. These expansions still solve the original Helmholtz equations for E and B because for a divergence-free field F, ∇ 2 (r ⋅ F) = r ⋅ (∇ 2 F). The resulting expressions for a generic electromagnetic field are: