Analytical Mechanics

Course Information

College	Akashi College	Year	2021
Course Title	Analytical Mechanics
Course Code	0014	Course Category	Specialized / Elective
Class Format	Lecture	Credits	Academic Credit: 2
Department	Architecture and Civil Engineering	Student Grade	Adv. 1st
Term	First Semester	Classes per Week	2
Textbook and/or Teaching Materials
Instructor	OGASAWARA Hiromichi

Course Objectives

(1) Understand that Lagrangian mechanics are formulated by developing Newtonian mechanics with a focus on the handling of constraints. (D)
(2) Understand the basic concepts of vibration in multi-degree of freedom systems (including continuum, which is an infinite degrees of freedom system), with a focus on normal vibration. (D), (F)
(3) Learn the calculus of variations, and understand that the basic laws of mechanics can be formulated as variation principles. (D), (H)
(4) Understand that Hamiltonian mechanics (a canonical transformation) are formulated by converting a motor equation, a second order differential equation, into a first order one. (D), (H)

Rubric

	Ideal Level	Standard Level	Unacceptable Level
Achievement 1	Fully understand the formulation of Lagrangian mechanics.	Understand the formulation of Lagrangian mechanics.	Do not understand the formulation of Lagrangian mechanics.
Achievement 2	Fully understand the basic concepts of multi-degree of freedom vibration systems.	Understand the basic concepts of multi-degree of freedom vibration systems.	Do not understand the basic concepts of multi-degree of freedom vibration systems.
Achievement 3	Fully understand the formulation of mechanics by variation principles.	Understand the formulation of mechanics by the variation principles.	Do not understand the formulation of mechanics by the variation principles.
	Fully understand the formulation of Hamiltonian mechanics.	Understand the formulation of Hamiltonian mechanics.	Do not understand the formulation of Hamiltonian mechanics.

Assigned Department Objectives

学習・教育目標 (D) See

学習・教育目標 (F) See

学習・教育目標 (H) See

Teaching Method

Outline:

　Analytical mechanics is the mathematical development of Newtonian mechanics and is one of the important fundamental departments involved in the wide area of engineering. The theory of analytical mechanics is composed of the Lagrangian and Hamiltonian mechanics (a canonical transformation). In this course, students will mainly study the Lagrangian. The Lagrangian mechanics is designed to foresee various mechanics problems and handle them well. It is also the basis for learning the Hamiltonian mechanics, which is introduced at the end of the semester.

Style:

　Classes are held in a lecture style.

Notice:

　This course's content will amount to 90 hours of study in total. These hours include the learning time guaranteed in classes and the standard self-study time required for pre-study / review, and completing assignment reports. Be aware that class time makes up a small percentage of the overall expected learning time, and students are advised to thoroughly pre-study or review.
Students who miss 1/3 or more of classes will not be eligible for a passing grade.

Characteristics of Class / Division in Learning

Active Learning	Aided by ICT	Applicable to Remote Class	Instructor Professionally Experienced

Course Plan

			Theme	Goals
1st Semester
	1st Quarter
		1st	The principle of virtual work and d'Alembert's principle	Learn the basics about the principle of virtual work and d'Alembert's principle.
		2nd	The method of Lagrange multipliers	Learn the basics of the method of Lagrange multipliers.
		3rd	Lagrange's motion equations of the first kind	Learn the basics of Lagrange's motion equations of the first kind.
		4th	Generalized coordinates and generalized speed	Learn the basics of generalized coordinates and generalized speed.
		5th	Lagrange's motion equations (the second kind)	Learn the basics of Lagrange's motion equations of the second kind.
		6th	Normal coordinates in a coupled oscillation system	Learn the basics of coupled oscillation systems.
		7th	Normal coordinates in a coupled oscillation system	Learn the basics of coupled oscillation systems.
		8th	Waves	Learn the basics of waves.
	2nd Quarter
		9th	Lagrangian continuum	Learn the basics of Lagrangian continuum.
		10th	Calculus of variations and Euler's differential equations	Learn the basics of the calculus of variations and Euler's differential equations.
		11th	Hamilton's principle	Learn the basics of Hamilton's principle.
		12th	Hamilton's canonical equations	Learn the basics of Hamilton's canonical equations.
		13th	Hamilton's canonical equations	Learn the basics of Hamilton's canonical equations.
		14th	Variation principles in Hamiltonian mechanics	Learn the basics of variation principles in Hamiltonian mechanics.
		15th	Summary and supplementary notes	Understand the relationship between Lagrangian and Hamiltonian mechanics.
		16th	Final exam

Evaluation Method and Weight (%)

	Examination	Exercise	Total
Subtotal	70	30	100
Basic Proficiency	0	0	0
Specialized Proficiency	70	30	100
Cross Area Proficiency	0	0	0