As soft robotics applications become more demanding, the control requirements also increase. In particular, agile trajectory tracking control requires new control concepts for soft robots. The main challenges in controlling soft robots are that soft robots are often underactuated and redundantly actuated at the same time. In addition, modeling is usually difficult due to large elastic deformations, unknown material parameters, and manufacturing inaccuracies. So far, in soft robotics mostly quasi-static modeling and control approaches are used. Models and controllers based on this assumption are called kinematic in the soft robotics community. In particular, data-driven models are very popular because they can easily incorporate manufacturing inaccuracies and unknown parameters if enough measurement data from the real robot is available. However, for more advanced soft robotics applications, faster and more accurate motions are required. This requires dynamics to be taken into account. A direct extension of existing data-driven kinematic models to a dynamic model is usually not possible due to the amount of training data required. Therefore, mechanical models are gaining importance for the description of the dynamics. In this contribution, the modeling and open-loop trajectory tracking control of a soft robot is presented. The model based on piecewise constant curvature is split into a kinematic and a dynamic part. This allows to use a more detailed model for the kinematics and a simpler model for the dynamics. This reduces the computational time and the amount of data required for parameter tuning without reducing the performance of the trajectory tracking control. The feedforward controller for the dynamic part is based on model inversion using the servo-constrains approach. Finally, the strength of this approach is demonstrated in experiments. Also, a comparison to alternative approaches is given.