An excerpt from the beginning of the first lecture. IN the following lectures it is proposed to consider certain interesting and important questions of dynamics from the standpoint of the theory of functions of the complex variable. I am to develop a new method, which, as I think, renders the discussion of these questions simpler and more attractive. My object in presenting it, however, is more general than that of throwing light on a particular class of problems in dynamics. I wish by an illustration which may fairly be ...
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An excerpt from the beginning of the first lecture. IN the following lectures it is proposed to consider certain interesting and important questions of dynamics from the standpoint of the theory of functions of the complex variable. I am to develop a new method, which, as I think, renders the discussion of these questions simpler and more attractive. My object in presenting it, however, is more general than that of throwing light on a particular class of problems in dynamics. I wish by an illustration which may fairly be regarded as representative to make evident the advantage which is to be gained by dynamics and astronomical and physical science in general from a more intimate association with the modern pure mathematics, the theory of functions especially. I venture to hope, therefore, that my lectures may interest engineers, physicists, and astronomers as well as mathematicians. If one may accuse mathematicians as a class of ignoring the mathematical problems of the modern physics and astronomy, one may, with no less justice perhaps, accuse physicists and astronomers of ignoring departments of the pure mathematics which have reached a high degree of development and are fitted to render valuable service to physics and astronomy. It is the great need of the present in mathematical science that the pure science and those departments of physical science in which it finds its most important applications should again be brought into the intimate association which proved so fruitful in the work of Lagrange and Gauss. I shall confine my discussion mainly to the problem presented in the motion of a top meaning for the present by a top" a rigid body rotating about an axis, when a single point in this axis, not the centre of gravity, is fixed in position. In the present lecture I shall present some preliminary considerations of a purely geometrical character. But it is necessary first of all to obtain an analytical representation of the rotation of a rigid body about a fixed point, and I shall begin with a statement of the methods ordinarily used....
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