This paper presents a framework for symmetry-guided multi-domain modeling based on the preservation of canonical structure. Using the co-Hamiltonian formalism with velocity and force as state variables, we derive motion equations that remain invariant under canonical transformations. We show that such transformations enable consistent mappings between physical variables across different domains—such as mechanical and fluidic systems—while preserving energy-conserving and causal structures. Furthermore, we demonstrate that generating functions systematically define these transformations, and that physical function models serve as graphical representations of the co-Hamiltonian dynamics and canonical transformations. This approach provides a theoretical foundation for structure-preserving, multi-domain modeling rooted in analytical mechanics.
Tanabe et al. (Wed,) studied this question.