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Classical Equations

  • Roman Jackiw
Chapter
Part of the CRM Series in Mathematical Physics book series (CRM)

Abstract

We begin with nonrelativistic equations that govern a matter density field ρ(t,r) and a velocity field vector v(t, r),taken in any number of dimensions. The equations of motion comprise a continuity equation,
$$\frac{\partial }{{\partial t}}\rho \left( {t,r} \right) + \nabla \cdot \left( {\rho \left( {t,r} \right)v\left( {t,r} \right)} \right) = 0,$$
(2.1)
which ensures matter conservation, that is, time independence, of N = ∫ dr ρ, and Euler’s equation, which is the expression of a nonrelativistic force law
$$\frac{\partial }{{\partial t}}v\left( {t,r} \right) + v\left( {t,r} \right) \cdot \nabla v\left( {t,r} \right) = f\left( {t,r} \right).$$
(2.2)

Keywords

Classical Equation Poisson Bracket Total Derivative Jacobi Identity Magnetic Surface 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 2002

Authors and Affiliations

  • Roman Jackiw
    • 1
  1. 1.Center for Theoretical PhysicsMassachusetts Institute of TechnologyCambridgeUSA

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