A Differential-Algebraic Framework for Inverse Variational Problems: A Rigorous Extension to Discrete Systems

Key Points

• This work aims to extend inverse variational problems to discrete systems using a differential-algebraic framework.
• Developed theory for constructing discrete variational principles from differential equations.
• Defined discrete inverse variational closure to provide algebraic foundations.
• Used algebraic expressions and validation algorithms for discrete Helmholtz conditions.
• Established a rigorous framework aiding in discrete variational integrals and geometric mechanics.
• Demonstrated effective handling of gauge freedom and symmetry restoration in discrete settings.