Analytical Mechanics

I will teach basics and applications of analytical mechanics emphasizing variation principle of statics, variation principle of dynamics, and method of variation. These issues will be applied to mechanics of rigid body systems and vibration, which are important topics in mechatoronics.

1st10/ 2Introduction: Newton mechanics vs analytical mechanics
2nd10/ 9Variational Principles: variation and variational principles
3rd10/14Variational Principles: variational principle in statics
4th10/16Variational Principles: statics under constraints
5th10/30Variational Principles: variational principle in dynamics
6th11/ 6Rigid Body Rotation: planar rotation
7th11/13Rigid Body Rotation: spatial rotation
8th11/20Rigid Body Rotation: quaternion
9th11/27Link Mechanisms: open link mechanism
10th12/ 4Link Mechanisms: closed link mechanism
11th12/11Elastic Deformation: elastic potential energy
12th12/18Elastic Deformation: finite element method (FEM)
13th12/25Elastic Deformatino: dynamic deformation
14th 1/15Inelastic Deformation: 1D inelastic deformation
15th 1/19Inelastic Deformation: 2D/3D inelastic deformation

1st    Introduction reduced copy
2nd-5th    Variational Principles reduced copy
6th-8th    Rigid Bidy Rotation reduced copy
9th,10th    Link Mechanisms reduced copy
11th-13th    Elastic Deformation reduced copy
14th,15th    Inelastic Deformation reduced copy

Sample programs (MATLAB)
ODE solver van_der_Pol.m solve_van_der_Pol.m
ODE solver (time adaptive) van_der_Pol.m solve_van_der_Pol_adaptive.m
minimization Rosenbrock.m min_Rosenbrock.m

Sample programs (C)
ODE solver rk.c rk.h van_der_Pol.c
compile : gcc -o van_der_Pol.out van_der_Pol.c rk.c -lm
run : ./van_der_Pol.out
see result : more van_der_Pol.dat
ODE solver (time adaptive) rkf.c rk.h van_der_Pol_rkf.c
minimization neldermead.c mat.c mat.h min_Rosenbrock.c
compile : gcc -o min_Rosenbrock.out min_Rosenbrock.c neldermead.c mat.c -lm

Evaluation: Reports. You will pass the examination when your total score exceeds 60 points.

Textbook: No textbook is specified. You are recommended to read the reference books
References: Analytical Dynamics : A New Approach  Robert E. Kalaba     Cambridge University Press
Analytical Dynamics Haim Baruh     McGraw-Hill Higher Education

You are requested to study Newton mechanics (classical mechanics). In addition, you should complete differential and integral calculus.