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. 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.

中文翻译：

---

光敏聚合物中光相互作用的几何精确连续谱框架I.变分设定

当例如偶氮苯分子被嵌入到聚合物基质中时，分子光开关允许光敏聚合物化合物在暴露于一定波长的光时机械地响应。光力学，即光活性聚合物中的光-物质相互作用，为例如光驱动致动器的远程和非接触式激活提供了广阔的前景。在一系列较早的贡献中，Oates等人。他开发了一种成功的连续体配方，用于捕获偶氮苯聚合物化合物的电气，电子和机械耦合问题，从而主要致力于几何线性化运动学。在此基础上，我们在此基于Dirichlet和汉密尔顿原理以及值得注意的汉密尔顿方程，探索几何精确连续体框架的变分设置。从而，在处理耗散情况时，我们通过适当地引入耗散电势求助于各种变体问题的增量版本。尤其是，即使对于能量充沛的情况，到目前为止，几何上精确的光机械的哈密顿设置仍未得到充分开发，这可以说是因为相应的拉格朗日式在狄拉克的意义上是退化的。而且，总的来说，耗散动力系统的哈密顿量设置本身就是一个不断争论的问题。在这项贡献中，通过提倡以光机械耗散情况为例的哈密顿设置的新型增量形式，我们的目标也是统一耗散动力系统的变分方法。在一起