query: Necessary and sufficient for vector field to be conservative
positive_passages.docid: 16293
positive_passages.text: N-dimensional generalization of vector curl from elements of Jacobian
negative_passages.docid: 33969
negative_passages.text: "Basis extension theorem" for local smooth vector fields
negative_passages.docid: 130166
negative_passages.text: Equivalece of the geodesic equation and the continuity equation for the energy-momentum tensor
negative_passages.docid: 66919
negative_passages.text: When/why does the principle of least action plus boundary conditions not uniquely specify a path?
negative_passages.docid: 150081
negative_passages.text: Deriving Lagrangian density for electromagnetic field
negative_passages.docid: 121495
negative_passages.text: Decompose vector fields on product manifolds
negative_passages.docid: 19453
negative_passages.text: Invariance of domain for manifold
negative_passages.docid: 67641
negative_passages.text: Why should field operators satisfy the classical equations of motion?
negative_passages.docid: 64247
negative_passages.text: Noether Theorem and Energy conservation in classical mechanics
negative_passages.docid: 28057
negative_passages.text: Deriving $p = mv$ from translational symmetry (momentum conservation law)?
negative_passages.docid: 35337
negative_passages.text: Problem in notation: $(\vec{v}\cdot\vec{\nabla})\vec{v}$ versus $L_v(\vec{v})$
negative_passages.docid: 38950
negative_passages.text: On the uniqueness of the Riemann-Christoffel tensor
negative_passages.docid: 126991
negative_passages.text: Prerequisites for classical mechanics by Susskind
negative_passages.docid: 56543
negative_passages.text: Do we fix divergence of the vector potential $A$, because $\nabla \cdot \nabla \psi \ne 0$?
negative_passages.docid: 33949
negative_passages.text: Leibniz Rule for Covariant derivatives
negative_passages.docid: 1045
negative_passages.text: Why is this vector field curl-free?
negative_passages.docid: 46358
negative_passages.text: geometric interpretation of $\vec v \cdot \operatorname{curl} \vec v = 0 $