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L1 Introduction

L1 Introduction - S Widnall 16.07 Dynamics Fall 2009...

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S. Widnall 16.07 Dynamics Fall 2009 Version 2.0 Lecture L1 - Introduction Introduction In this course we will study Classical Mechanics and its application to aerospace systems. Particle motion in Classical Mechanics is governed by Newton’s laws and is sometimes referred to as Newtonian Mechanics. The motion of extended rigid bodies is analyzed by application of Newton’s law to a multi-particle system. These laws are empirical in that they combine observations from nature and some intuitive concepts. Newton’s laws of motion are not self evident. For instance, in Aristotelian mechanics before Newton, a force was thought to be required in order to maintain motion. Much of the foundation for Newtonian mechanics was laid by Galileo at the end of the 16th century. Newton, in the middle of the 17th century stated the laws of motion in the form we know and use them today, and shortly after, he formulated the law of universal attraction. This led to a complete theory with which he was able to explain many observed phenomena, in particular the motion of the planets. Nevertheless, these laws still left many unanswered questions at that time, and it was not until later years that the principles of classical mechanics were deeply studied and rationalized. In the eighteenth century, there were many contributions in this direction, such as the principle of virtual work by Bernoulli, D’Alambert’s principle and the theory of rigid body dynamics developed by Euler. In the nineteenth century, Lagrange and later Poisson, Hamilton and Jacobi developed the so called analytical or rational mechanics and gave to the theory of Newtonian mechanics a much richer mathematical structure. Classical Mechanics has its limitations and breaks down where more modern theories such as relativity and quantum mechanics, developed in the twentieth century, are successful. Newtonian mechanics breaks down for systems moving at speeds comparable with the speed of light, and also fails for systems of dimensions comparable to the size of the atom. Nevertheless, for practical engineering applications, Newtonian mechanics provides a very good model to represent reality, and, in fact, it is hard to find examples in aerospace where Newtonian mechanics is not adequate. The most notable perhaps are the relativistic corrections that need to be made for modeling satellite communications. 16.07’s Place in the Aero-Astro Curriculum Aero-Astro focuses on the analysis, design and control of aerospace vehicles, both aircraft and space craft and the environment in which they are used. The place of 16.07 within the overall curriculum is shown in Figure 1. 1
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16.07 is a core discipline of aerospace engineering: dealing with the natural dynamics of aero-astro systems.
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L1 Introduction - S Widnall 16.07 Dynamics Fall 2009...

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