Introduction to Analytical Mechanics
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In our eReader you can find the full English version of the book. Read Introduction to Analytical Mechanics Online - link to read the book on full screen. Our eReader also allows you to upload and read Pdf, Txt, ePub and fb2 books. In the Mini eReder on the page below you can quickly view all pages of the book - Read Book Introduction to Analytical Mechanics
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the acceleration produced by a unit of mass in a unit of mass at unit distance (see Arts. 245, 246).
The best test of this hypothesis as an actual law of physical nature is found in the close agreement of the results of theoretical astronomy based on this law with the observed celestial phenomena.
307. Taking Newton's law as a basis, let us now turn to the converse problem of determining the motion of a particle acted upon by a single central force for which f{r) = /i/r^ (problem of planetary m...otion).
It has been shown in Kinematics (Arts. 109-112) that if the force be attractive, the particle will describe a conic section with one of the foci at the center of force, the conic being an ellipse, parabola, or hyperbola, according as .„^g^^ (13) // the force he repulsive, the same reasoning will apply, except that fi is then a negative quantity. The orbit is, therefore, in this case always hyperbolic; the branch of the hyperbola that forms the orbit must evidently turn its convex side towards the focus at which the center of force is situated, since the force always lies on the concave side of the path.
What to read after Introduction to Analytical Mechanics?
You can find similar books in the "Read Also" column, or choose other free books by Alexander Ziwet to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
the acceleration produced by a unit of mass in a unit of mass at unit distance (see Arts. 245, 246).
The best test of this hypothesis as an actual law of physical nature is found in the close agreement of the results of theoretical astronomy based on this law with the observed celestial phenomena.
307. Taking Newton's law as a basis, let us now turn to the converse problem of determining the motion of a particle acted upon by a single central force for which f{r) = /i/r^ (problem of planetary m...otion).
It has been shown in Kinematics (Arts. 109-112) that if the force be attractive, the particle will describe a conic section with one of the foci at the center of force, the conic being an ellipse, parabola, or hyperbola, according as .„^g^^ (13) // the force he repulsive, the same reasoning will apply, except that fi is then a negative quantity. The orbit is, therefore, in this case always hyperbolic; the branch of the hyperbola that forms the orbit must evidently turn its convex side towards the focus at which the center of force is situated, since the force always lies on the concave side of the path.
What to read after Introduction to Analytical Mechanics?
You can find similar books in the "Read Also" column, or choose other free books by Alexander Ziwet to read onlineMoreLess
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