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This study explores energy loss in particles due to gravity under non-holonomic constraints, extending physics principles beyond holonomic limitations. Findings confirm energy dissipation and align with continuum mechanics for broader applicability.

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Area of Science:

  • Theoretical Physics
  • Classical Mechanics
  • Continuum Mechanics

Background:

  • The least action principle is fundamental in modern physics but limited to holonomic constraints.
  • Investigating physics under non-holonomic constraints is crucial for broader theoretical development.

Purpose of the Study:

  • To investigate energy loss of particles interacting gravitationally in a medium with non-holonomic constraints.
  • To extend the applicability of physical principles to systems with non-holonomic constraints.
  • To analyze energy dissipation for arbitrary particles, with a specific focus on photons.

Main Methods:

  • Calculation from first principles using the principle of virtual work.
  • Application of d'Alembert principle for analyzing forces under constraints.
  • Utilizing continuum mechanics and the Euler-Cauchy stress principle for an alternative derivation.

Main Results:

  • Established the dissipative nature of energy loss under non-holonomic constraints.
  • Derived the energy lost by arbitrary particles, including a specific result for photons.
  • Confirmed consistency between the first-principles derivation and the continuum mechanics approach.

Conclusions:

  • The study successfully extends the analysis of energy loss to non-holonomic systems.
  • The findings demonstrate the dissipative effects of gravitational interaction under these constraints.
  • The agreement with continuum mechanics validates the robustness of the derived formalism.