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Unified expressions of all differential variational principles. (English) Zbl 1046.70010
Summary: We give a mathematical expression of the quantitative causal principle. Using this expression, we derive unified expressions for D’Alembert-Lagrange, virtual work, Jourdain, Gauss and general D’Alembert-Lagrange principles of differential type. We find the intrinsic relations among these variational principles, the conservation quantities of the above principles, and finally obtain the Noether conservation laws for all these variational principles in the systems with the symmetry of Lie group $$D_m$$.

##### MSC:
 70H30 Other variational principles in mechanics 70H33 Symmetries and conservation laws, reverse symmetries, invariant manifolds and their bifurcations, reduction for problems in Hamiltonian and Lagrangian mechanics 49S05 Variational principles of physics (should also be assigned at least one other classification number in Section 49-XX)
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