Soft robotic manipulators are on the verge to their first real applications. In most cases they are actuated by fluidic pressure or tendons and molded of highly elastic material, which performs large deformation if put under stress. Performing tasks e.g. in inspection of narrow machines or endoscopy requires the actuator to be tactile and controllable. Due to their highly nonlinear behavior, model-based approaches are investigated to combine and utilize sensor information to estimate the system states of the manipulator. In this paper, equations of motion (EoM) for the well-known piecewise constant curvature (PCC) approach are extended by a floating base as it is often used in kinematic chains for legged robots and their contact with the ground. Base reaction forces and moments, which are easily measurable quantities, become visible in the EoM, if the six spatial degrees of freedom at the base of the manipulator are considered. Thereby, additional information on the system's states is obtained and used in the proposed identification scheme. Essentially, the floating base, a center-of-gravity approach and a state-of-the-art parametrization of the PCC kinematics are combined to derive and validate a Lagrangian dynamics model. On a best-case set of validation step responses, the identified inverse dynamics model performs with an accuracy of 5% to 7.6% of max. actuation torque.© 2022 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works