Inertial Measurement Units (IMUs) enable portable, multibody motion capture (MoCap) in diverse environments beyond the laboratory, making them a practical choice for diagnosing mobility disorders and supporting rehabilitation in clinical or home settings. However, challenges associated with IMU measurements, including magnetic distortions and drift errors, complicate their broader use for MoCap. In this work, we propose a tightly coupled motion capture approach that directly integrates IMU measurements with multibody dynamic models via an Iterated Extended Kalman Filter (IEKF) to simultaneously estimate the system's kinematics and kinetics. By enforcing kinematic and kinetic properties and utilizing only accelerometer and gyroscope data, our method improves IMU-based state estimation accuracy. Our approach is designed to allow for incorporating additional sensor data, such as optical MoCap measurements and joint torque readings, to further enhance estimation accuracy. We validated our approach using highly accurate ground truth data from a 3 Degree of Freedom (DoF) pendulum and a 6 DoF Kuka robot. We demonstrate a maximum Root Mean Square Difference (RMSD) in the pendulum's computed joint angles of 3.75 degrees compared to optical MoCap Inverse Kinematics (IK), which serves as the gold standard in the absence of internal encoders. For the Kuka robot, we observe a maximum joint angle RMSD of 3.24 degrees compared to the Kuka's internal encoders, while the maximum joint angle RMSD of the optical MoCap IK compared to the encoders was 1.16 degrees. Additionally, we report a maximum joint torque RMSD of 2 Nm in the pendulum compared to optical MoCap Inverse Dynamics (ID), and 3.73 Nm in the Kuka robot relative to its internal torque sensors.