Liquid crystal elastomers (LCEs) typically exhibit slow deformation in response to environmental stimuli. However, recent studies have demonstrated that when LCE is reduced to a fiber form, it can undergo rapid and reversible contractions. This unique property allows LCE fibers to convert light energy into fast mechanical motion, enabling them to act as actuators that can swiftly flip the wings or lift an object. In this paper, we present a theoretical investigation of a three-dimensional pendulum constructed by a LCE fiber, which differs from the conventional pendulum with a fixed string length. The string length of the LCE pendulum is time-dependent and responsive to light radiation. We develop a nonlinear dynamic model based on Lagrangian mechanics and the photodynamic theory of LCE to study the effects of initial conditions, light intensity, radiation region, damping factor, and gravity on the characteristics of the three-dimensional pendulum. Our findings reveal the existence of three distinct modes of motion: static, light-excited self-oscillation, and light-excited self-rotation. We elucidate the mechanisms underlying these modes by investigating the time-dependent length of the string, the forces acting on the string, and the work done by light radiation during each period. The results and dynamic model presented in this paper provide valuable insights into light-driven motion structures and offer references for the design of soft robotics, energy harvesting devices, and wing-flapping micro aircraft applications based on smart soft materials.
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