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MAS313 Advanced Dynamics

Course description for academic year 2022/2023

Contents and structure

In this course, students study the dynamics of gears, contact, rolling, inertial guidance systems, cranes on ships, and fundamental robotic systems. To accomplish this, this course introduces advanced mathematics in a distilled and controlled style. The course applies the math to the study of machines and mechanisms. This course also introduces students to the foundations of 3D graphics programming to visualize the motion of machines. Finally, this course introduces students to computational methods to prepare them for advanced work in mechanical engineering analysis. The skills in this class are basic to several to subjects at the Department of Machine and Marine Engineering, to an engineering career, and to life-long learning.



  1. The study of collisions: rolling, gears, contact.
  2. Modal analysis of machine components.
  3. Study of vibrations of structures and mechanical devices.
  4. The Special Euclidean Group of Lie Group Theory.
  5. Hamilton¿s equation and the Lagrangian to solve dynamical systems.
  6. Restricted variation of angular velocity.
  7. Dynamics of linked systems.
  8. Numerical Methods (Runge-Kutta, Cayleigh Hamilton).
  9. Decode a complete Matlab code that implements the dynamics of a linked system.
  10. Decode a complete 3D graphics code to study physics-based graphical simulations.

Learning Outcome

After completing MAS115 the student will have:

Competence-Students will gain fundamental knowledge:

  • A fundamental understanding of second order differential equations.
  • A fundamental understanding of modal analysis methods: eigenvalues and eigenvectors.
  • A fundamental understanding of the calculus of variations.
  • A fundamental understanding of computer methods in engineering.

Skills-With the aforementioned foundation, student will acquire the following skills:

  • An ability to solve second order differential equations for vibrations of mechanical devices.
  • An ability to obtain approximate solutions: modal analysis of mechanical devices.
  • An ability to formulate the Lagrangian for Hamilton`s Principle in dynamics.
  • An ability to code the solutions of the equations of motion of dynamical systems.

Knowledge-Using the aforementioned skills, student will gain experience with mechanical systems

  • Experience with the basic concepts of advanced dynamics of linked robotics and free bodies.
  • Experience with the mechanics of inertial guidance systems and control.
  • Experience with contact constraints.
  • Experience with aspects of advanced mathematics and its role in analyzing mechanical engineering mechanisms: rolling without slipping, gears, linked systems.
  • Experience with the role of computers in solving advanced equations of motion for various engineering mechanism.
  • Experience to undertake studies in an appropriate Master`s Degree program.

Entry requirements


Recommended previous knowledge

Dynamics (MAS112), Basic Engineering Mathematics (MAT100/MAT110) and Advanced Mathematics (MAT107/MAT203/MAT202).

Teaching methods

Lectures. Mandatory and voluntary exercises. Exercises with guidance.

Compulsory learning activities

8 of 10 compulsory exercises (submission) must be completed (alone) and approved in order to take the examination.


4 hour written exam. Letter grade A to F

Examination support material

Drawing and writing materials

Basic calculator according to the regulations at Western Norway University of Applied Sciences.

More about examination support material

Course reductions

  • MAS115 - Advanced dynamics - Reduction: 10 studypoints