## Course Title : Fundamental Mechanics

Code 35040 2nd year 1st term Monday・4 Kyoutsuu4 2 English An

### Course Description

Newtonian mechanics and its application to engineering are interpreted with concentration on single particle, multi-partical system and rigid body. Especially,some mathematical approaches necessary for mechanics are introduced based on those mathematical knowledge learned in the first academic year. Meanwhile, the relationship between mechanical interpretation and mathematical treatment of some classical problems are specifically emphasized. Study of this lecture would not only make the students grasp basic principles of mechanics but also think more logically and systematically.

Grade is evaluated based on the final examination and assignments.

### Course Goals

As an intermediate course in mechanics at undergraduate level, this course aims at training students to think about mechanical phenomena in mathematical terms, developing an intuition for the precise mathematical formulation of mechanical problems and for the mechanical interpretation of the mathematical solutions.

### Course Topics

Theme Class number of times Description
Kinematics of a single particle in space 2 algebra and calculus of vectors
tangent and normal vectors to a curve
definition of velocity and acceleration in 2-D motion by plane polar coordinates
definition of velocity and acceleration in 3-D motion by cylindrical polar coordinates and spherical polar coordiantes
laws of motion 3 Newton's laws of motion
discussion of the general problem of 1-D motion
linear differential equations with constant coefficient
linear oscillations,resonance,principle of superposition
discussion of the general problem of 2-D and 3-D motion
Problems in particle dynamics 1 the Law of Gravitation
center of mass and center of gravity
motion through a resisting medium
constrained motion
energy conservation 2 energy theorems
definition of potential energy, conservative force
conservation of mechanical energy in 3-D conservative field
energy conservation in constrained motion
motion of a system of particles 2 degrees of freedom, energy principle
linear momentum principle, conservation of linear momentum, collision theory and two-body scattering
angular momentum principle, conservation of angular momentum
Rotating reference frames 1 transformation formulae
particle dynamics in a non-frame
motion relative to the Earth
multi-particle system in a non-inertial frame
motion of rigid body 2 dynamical problem of the motion of a rigid body
statics of rigid bodies
statics of structures
equilibrium of flexible strings and cables
equilibrium of solid beams
angular momentum of a rigid body
inerital and stress tensors
foundation of analytical mechanics 1 Constraint condition,constraint force, generalized coordinate, generalized for, Lagrange's equations
confirmation of achievement 1 The achievement assessment is intended to measure students' knowlege, skill and aptitude on the subject using quiz and viva-voce.

### Textbook

R.DOUGLAS GREGORY: Classical Mechanics, Cambridge University Press, 2006 ### Textbook(supplemental)

Keith R.Symon: Mechanics, Third Edition, Addision-Wesley, 1971 Fedinand P.Beer, E.Russell Johnston, etc.: Mechanics for Engineers, Dynamics, McGraw Hill, 2007 ### Prerequisite(s)

calculus A and B, Linear Algebra A and B