Molecular photo-switches as, e.g., azobenzene molecules allow, when embedded into a polymeric matrix, for photo-active polymer compounds responding mechanically when exposed to light of certain wavelength. Photo-mechanics, i.e. light-matter interaction in photo-active polymers holds great promise for, e.g., remote and contact-free activation of photo-driven actuators. In a series of earlier contributions, Oates et al. developed a successful continuum formulation for the coupled electric, electronic and mechanical problem capturing azobenzene polymer compounds, thereby mainly focussing on geometrically linearized kinematics [1, 2, 3]. Building on that formulation, we here explore the variational setting of a geometrically exact continuum framework based on Dirichlet’s and Hamilton’s principle as well as, noteworthy, Hamilton’s equations. Thereby, when treating the dissipative case, we resort to incremental versions of the various variational problems via suited incorporation of a dissipation potential. In particular, the Hamiltonian setting of geometrically exact photo-mechanics is up to now largely under-explored even for the energetic case, arguably since the corresponding Lagrangian is degenerate in Dirac’s sense. Moreover, in general, the Hamiltonian setting of dissipative dynamical systems is a matter of ongoing debate per se. In this contribution, by advocating a novel incremental version of the Hamiltonian setting exemplified for the dissipative case of photo-mechanics, we aim to also unify the variational approach to dissipative dynamical systems. Taken together, the variational setting of a geometrically exact continuum framework of photo-mechanics paves the way for forthcoming theoretical and numerical analyses.

分子光开关，例如偶氮苯分子，当嵌入到聚合物基质中时，允许光活性聚合物化合物在暴露于特定波长的光时进行机械响应。光力学，即光敏聚合物中的光-物质相互作用，对于例如光驱动致动器的远程和非接触激活具有广阔的前景。在一系列早期的贡献中，Oates 等人。为捕获偶氮苯聚合物化合物的耦合电气、电子和机械问题开发了一个成功的连续体公式，从而主要关注几何线性化运动学 [1, 2, 3]。在该公式的基础上，我们在这里探索了基于狄利克雷和汉密尔顿原理以及值得注意的汉密尔顿方程的几何精确连续体框架的变分设置。从而，在处理耗散情况时，我们通过适当地结合耗散势来求助于各种变分问题的增量版本。特别是，几何上精确的光力学的哈密顿设置到目前为止即使对于能量情况也基本上没有得到充分探索，可以说是因为相应的拉格朗日量在狄拉克的意义上是退化的。此外，一般而言，耗散动力系统的哈密顿设置本身就是一个持续争论的问题。在这个贡献中，通过提倡以光力学耗散情况为例的哈密顿设置的新增量版本，我们的目标是统一耗散动力系统的变分方法。综合起来，