... iPrinter: Opaque this A Mathematical Introduction to Fluid Mechanics Alexandre ChorinDepartment of MathematicsUniversity of California, BerkeleyBerkeley, California 94720-3840, USAJerrold E. MarsdenControl ... that is, if x(s)isastreamline at the instantt,itisacurve parametrized by a variable, say s, that satisfiesdxds= u(x(s),t),tfixed.We define a fixed trajectory to be the curve traced out by a particleas ... of ρ (and therefore3One can carry this even further and use balance of energy and its invariance underEuclidean motions to derive balance of momentum and mass, a result of Green andNaghdi....