Classical Equations

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


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,
$$\frac{\partial }{{\partial t}}\rho \left( {t,r} \right) + \nabla \cdot \left( {\rho \left( {t,r} \right)v\left( {t,r} \right)} \right) = 0,$$
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
$$\frac{\partial }{{\partial t}}v\left( {t,r} \right) + v\left( {t,r} \right) \cdot \nabla v\left( {t,r} \right) = f\left( {t,r} \right).$$


Classical Equation Poisson Bracket Total Derivative Jacobi Identity Magnetic Surface 
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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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