Herglotz type Lagrange equations and Noether symmetry and conserved quantity for mechanical systems with variable mass

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    Herglotz’s variational principle provides a variational description of nonconservative dissipation problems, and variable mass mechanics is widely used in nature and engineering. Therefore, it provides a new way to study variable mass mechanics by applying Herglotz’s variational principle to Lagrange equations and conservation laws of variable mass mechanics systems. In this paper, the Herglotz type generalized variational principle of mechanical systems with variable mass is established and the Herglotz type Lagrange equations of mechanical systems with variable mass are derived. Herglotz type Noether symmetry of variable mass mechanical systems is defined, and the Herglotz Noether theorem and its inverse theorem are established and proved. At the end of this paper, two concrete examples of nonconservative systems with variable mass are given to illustrate the application of the results.

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  • Received:January 14,2022
  • Revised:March 26,2022
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  • Online: December 24,2022
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