Efficient formulations for the dynamics of continuum robots are necessary to enable accurate modeling of the robot's shape during operation. Previous work in continuum robotics has focused on low-fidelity lumped parameter models, in which actuated segments are modeled as circular arcs, or computationally intensive high-fidelity distributed parameter models, in which continuum robots are modeled as a parameterized spatial curve. In this paper, a novel dynamic modeling methodology is studied that captures curvature variations along a segment using a finite set of kinematic variables. This dynamic model is implemented using the principle of virtual power (also called Kane's method) for a continuum robot. The model is derived to account for inertial, actuation, friction, elastic, and gravitational effects. The model is inherently adaptable for including any type of external force or moment, including dissipative effects and external loading. Three case studies are simulated on a cable-driven continuum robot structure to study the dynamic properties of the numerical model. Cross validation is performed in comparison to both experimental results and finite-element analysis.