# Syllabus 2014

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## Course Title : Fundamental Mechanics

Code | 35040 |
---|---|

Course Year | 2nd year |

Term | 1st term |

Class day & Period | Monday・4 |

Location | Kyoutsuu4 |

Credits | 2 |

Restriction | |

Lecture Form(s) | |

Language | English |

Instructor | 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.

### Grading

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 rotation about an axis 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