Basics of the Lagrangian FieldTheory.- Lagrangian Field Theory with the Non-commuting (NC)Variations.- Vertical Connections in the Congurational Bundle and theNCvariations.- K-twisted Prolongations and -symmetries (by Works ofMuriel,Romero.- Applications: Holonomic and Non-Holonomic Mechanics,H.KleinertAction Principle, Uniform Materials,and the Dissipative Potentials.- Material Time,NC-variations and the Material Aging.- Fiber Bundles and Their GeometricalStructures, Absolute Parallelism.- Jet Bundles, Contact Structures andConnections on Jet Bundles.- Lie Groups Actions on the Jet Bundles and theSystems of Differential Equations.
Non-commuting Variations in Mathematics and Physics
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Basics of the Lagrangian FieldTheory.- Lagrangian Field Theory with the Non-commuting (NC)Variations.- Vertical Connections in the Congurational Bundle and theNCvariations.- K-twisted Prolongations and -symmetries (by Works ofMuriel,Romero.- Applications: Holonomic and Non-Holonomic Mechanics,H.KleinertAction Principle, Uniform Materials,and the Dissipative Potentials.- Material Time,NC-variations and the Material Aging.- Fiber Bundles and Their GeometricalStructures, Absolute Parallelism.- Jet Bundles, Contact Structures andConnections on Jet Bundles.- Lie Groups Actions on the Jet Bundles and theSystems of Differential Equations.
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