## Elements of Newtonian MechanicsThis book is intended as a textbook for an entry-level university course in Newtonian mechanics for students of physics, astronomy, and the engineering sciences. The material has been used as a first-semester text for first-year undergraduates at the Niels Bohr Institute, which is part of the University of Copenhagen. Our way of presenting Newtonian mechanics is influenced by the writings of the late Max Born. Also, the Feynman Lectures on Physics have been an important source of inspiration. In fact, the idea for the book came when we read Section 16.1 of Volume 1 of the Feynman Lectures. Ideas from the well-known Berkeley Physics Course may also be traced in the text. All of the books quoted in the literature list have, in one way or another, served as a source for our lectures for undergraduates. It is assumed that the students already have a rudimentary knowledge of Newtonian mechanics, say at the high-school level. Some background in vectors and elementary calculus is also required, i.e., the students should know how to add vectors as well as how to differentiate and integrate elementary functions. The Appendix contains the required background for the use of vectors in Newtonian mechanics. |

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### Contents

1 | |

Newtons Five Laws | 27 |

Gravitational and Inertial Mass | 73 |

The Galilei Transformation | 83 |

The Motion of the Earth 95 | 94 |

Motion in Accelerated Reference Frames | 101 |

The Problem of Motion | 153 |

Energy | 167 |

The Angular Momentum Theorem 219 | 218 |

Rotation of a Rigid Body | 237 |

The General Motion of a Rigid Body | 301 |

The Motion of the Planets | 333 |

Harmonic Oscillators | 373 |

Appendix Vectors and Vector Calculus 395 | 394 |

Selected References | 401 |

410 | |

### Other editions - View all

Elements of Newtonian Mechanics: Including Nonlinear Dynamics Jens M. Knudsen,Poul G. Hjorth Limited preview - 2012 |

Elements of Newtonian Mechanics: Including Nonlinear Dynamics Jens M. Knudsen,Poul G. Hjorth Limited preview - 2002 |

Elements of Newtonian Mechanics: Including Nonlinear Dynamics Jens M. Knudsen,Poul Hjorth Limited preview - 2012 |

### Common terms and phrases

absolute space angle angular momentum theorem angular velocity assume axis ball block Brahe bullet Calculate called center of mass centrifugal force circular orbit collision component Consider constant coordinate frame coordinate system Coriolis force denoted Determine direction disk distance Earth equation of motion equilibrium Example expression external forces fictitious forces Figure fixed stars force F force field forces acting frictional force frictionless galaxy Galileo gravitational field gravitational force harmonic oscillations heliocentric frame heliocentric reference frame homogeneous horizontal inertial frame inertial mass integration Kepler kinetic energy lab frame magnitude Mars Moon Newton Newton’s second law Newtonian mechanics observer pendulum perpendicular physical planet position potential energy Problem radius reaction force rest relative rigid body rotation relative rotation vector satellite solar system solution sphere string force surface third law tidal forces torque uniform circular motion velocity relative vertical z-axis zero