The paper proposes a Lagrangian formalism for describing the space-time dynamics of complex continuum motion with addition variables-non-Eulerian dynamic degrees of freedom. The new variables are interpreted in terms of mechanics and geometry, and principles are suggested for their tracking in experiments. The formalism offers invariant tensor representations of Lagrangians in a system with an extended set of independent variables, explains the mechanical meaning of their respective coefficients, and gives Euler-Lagrange equations for this type of multidimensional variational problems. It is hypothesized that the bundle geometry of dynamic degrees of freedom is a generalized structure for fluctuation and other models of complex continuum evolution. The proposed method is analyzed as applied to dynamic equations of developed turbulence, and an interpretation on its basis is given to turbulence degeneration into unsteady Euler fields.
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