2025 (Current Year) Faculty Courses School of Engineering Undergraduate major in Mechanical Engineering
Fundamentals of Analytical Dynamics (Mechanical Engineering)
- Academic unit or major
- Undergraduate major in Mechanical Engineering
- Instructor(s)
- Yutaka Nakano
- Class Format
- Lecture
- Media-enhanced courses
- -
- Day of week/Period
(Classrooms) - Class
- -
- Course Code
- MEC.D231
- Number of credits
- 100
- Course offered
- 2025
- Offered quarter
- 4Q
- Syllabus updated
- Mar 19, 2025
- Language
- Japanese
Syllabus
Course overview and goals
【Course description】
The course teaches the method for deriving the equations of motion using scalar quantities (the kinetic energy, the potential energy, virtual work).
【Aims】
The basic equations and equations of motion are required in various engneering field, and the ability to derive these equations based on general approach is vital. Students learn the method for deriving the equations of motion using Lagrangian equation of motion. This will allow them to understand mechanical phenomena deeply and they will be able to solve general problems in mechanics.
Course description and aims
By the end of this course, students will be able to:
1) Explain the constraint in mechanical systems and generalized coordinates.
2) Explain the principle of virtual work and D'Alembert's principle.
3) Derive Lagrangian equations of motion using the principle of virtual work and D'Alembert's principle.
4) Derive the equations of motion using Lagrangian equations of motion.
5) Explain the relationship between Hamilton's principle and Lagrangian equations of motion.
Keywords
Generalized coordinates，Principle of virtual work，D'Alembert's principle，Lagrangian equations of motion
Competencies
- Specialist skills
- Intercultural skills
- Communication skills
- Critical thinking skills
- Practical and/or problem-solving skills
- This class aims at learning 6 and 7 of learning objective.
Class flow
At the beginning of each class, overview and highlights of the previous class are reviewed. Towards the end of class, students are given exercise problems related to the lecture given that day to solve.
Course schedule/Objectives
| Course schedule | Objectives | |
|---|---|---|
| Class 1 | Characteristics and advantages of analytical dynamics | Review work and the law of the conservation of energy. |
| Class 2 | Principle of virtual work and D'Alembert's principle | Understand the principle of virtual work and D'Alembert's principle. |
| Class 3 | Derivation of Lagrangian equations of motion | Derive Lagrangian equations of motion using the principle of virtual work and D'Alembert's principle. |
| Class 4 | Derivation of equations of motion using Lagrangian equations of motion | Derive the equations of motion using Lagrangian equations of motion for multiple degrees of freedom system. |
| Class 5 | Lagrangian equations of motion with constraints | Derive the Lagrangian equations of motion with constraints using Lagrangian undetermined factors. |
| Class 6 | Variational principle and Euler-Lagrange equations | Understand the relationship between variational principle and Euler-Lagrange equations. |
| Class 7 | Hamilton's principle and Lagrangian equations of motion | Understand the relationship between Hamilton's principle and Lagrangian |
Study advice (preparation and review)
To enhance effective learning, students are encouraged to spend approximately 100 minutes preparing for class and another 100 minutes reviewing class content afterwards (including assignments) for each class.
They should do so by referring to textbooks and other course material.
Textbook(s)
None required.
Reference books, course materials, etc.
Upload course materials to T2SCHOLA.
Dover Publications，『The variational principles of mechanics / by Cornelius Lanczos』，ISBN-13: 9780486650678，
Evaluation methods and criteria
To be evaluated based on the final exam(80％) and the assignments(20％) given during the lecture. When the final exam is not available, to be evaluated based on the assignments given during the lecture.
Related courses
- MEC.A201 ： Engineering Mechanics
- MEC.B211 ： Ordinary Differential Equations
- MEC.D201 ： Mechanical Vibrations
Prerequisites
Students must have successfully completed Engineering Mechanics(MEC.A201) and Mechanical Vibrations (MEC.D201.R) or have equivalent knowledge.