• Introduces a unified dynamic modeling method for generalized space-deployable mechanisms using the local frame of the SE(3) Lie group, effectively handling both rigid and flexible links.
• Derives equations of motion via Hamilton's principle, yielding a constant mass matrix in the local frame for compact and unified dynamic equations.
• Employs a Lie group generalized-α time integration method to ensure numerical stability and efficiency for multibody systems with large rotations and deformations.
• Demonstrates the formulation through two numerical examples, showing accurate motion responses under varying configurations and loading conditions, broadening the application of Lie group methods in space mechanisms.