Dynamics of Mechanical Systems


The objective of this course is to convey the fundamental concepts of dynamics of multiple body systems, thus allowing the development and analysis of mechanical systems used in different industrial applications. from mechanisms in general to biomechanics, robotics and vehicles.

The aim is thus to instruct students about the potentialities and limitations of numerical models constructed from the programming of equations of motion with Cartesian or other formulations, either by the use of commercial codes, promoting their rational and appropriate use with regard to representation of real systems and their components.

General characterization





Responsible teacher

Marta Isabel Pimenta Verdete da Silva Carvalho, Pedro Samuel Gonçalves Coelho


Weekly - 4

Total - 80

Teaching language



Available soon


1.   Nikravesh, P. E. (2018). Planar Multibody Dynamics: Formulation, Programming with MATLAB®, and Applications. CRC Press.

2. Computer Aided Analysis of Mechanical Systems: Parviz Nikravesh, 1988 Prentice – Hall Publishers. Englewod Cliffs, New Jersey.

Teaching method

Classes are theoretical and practical, in a classroom equipped with computers and appropriate software. The concepts are taught through the theoretical exposition of the formulation and practical resolution of some type problems, by the computational implementation in code developed by the student or by the use of existing commercial software to compare or to implement more complex engineering cases.

Evaluation method

The evaluation is made through the appreciation of three practical assignments to be done individually by the students.

Score = 0.3 T1 + 0.35 T2 + 0.35 TF

T1 and T2 are assignments to be carried out during the class period, and a report will be prepared in a PowerPoint presentation format to be delivered along with the remaining files created to solve the problems mentioned. Students present their solution in class.

TF is the final work, with the statement constructed by the student and the report prepared with a text editor. The report must be delivered together with all the files created to solve the stated problem.

Subject matter

1. Introduction: Concepts of mechanism, kinematic joint, rigid body and flexible body. Two-dimensional and three-dimensional analysis.

2. Kinematic analysis: Relative coordinates. Equations of constraints, velocities and accelerations. Coordinate Partition Method. Motor constraints.

3. Planar kinematics with Cartesian coordinates: Coordinates, constraints and joints. Equations of position, velocity and acceleration. Kinematic joints. Applications.

4. Dynamic analysis in the plane: Equations of motion. Forces vector. Spring-damper-translation and rotation actuator. Reactions due to constraints. Lagrange Multipliers. System of equations of motion. Applications.

5. Numerical methods for solving ordinary differential equations.

6. Contact and impact of mechanical systems. Applications to motor vehicle collisions.

7. Other formulations used for dynamic multibody analysis.


Programs where the course is taught: