A Treatise On Dynamics of a Particle, With Numerous Examples
A Treatise On Dynamics of a Particle, With Numerous Examples
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Digitized by VjOOQIC 128 CENTRAL ORBITS.
149i A particle is projected from a given point in a given direction ana with a given velocity , and moves under the action of a central attraction varying inversely as the square of 'the distance; to determine the orbit We have P=s fiu*, and therefore 351+.-J.-0, the integral of which is tt-^ = ^cos(5 + 5), or, as it is^ usually written, u=^^{l+ecos{0-a)} (1).
This gives 5fl'*""l^^^"^ (^ — a) (2).
Let It be the distance of the point of projection from t...he center; /8 the angle, and Fthe velocity, of projection ; then when ^ = 0, «"5' ^«*^=-SSL- Hence, by (1), —^ — 1 = 6 cos a, .and, by (2), ~».^^* )8 = - e sin a.
From these^ tan a= —75 — f!
•(3).
h* ,« 2/* and **=';?^jJ,e>l, and the orbit is a hyperbola, F*=^, e = l, a parabola, F*
What to read after A Treatise On Dynamics of a Particle, With Numerous Examples?
You can find similar books in the "Read Also" column, or choose other free books by Peter Guthrie Tait to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
Digitized by VjOOQIC 128 CENTRAL ORBITS.
149i A particle is projected from a given point in a given direction ana with a given velocity , and moves under the action of a central attraction varying inversely as the square of 'the distance; to determine the orbit We have P=s fiu*, and therefore 351+.-J.-0, the integral of which is tt-^ = ^cos(5 + 5), or, as it is^ usually written, u=^^{l+ecos{0-a)} (1).
This gives 5fl'*""l^^^"^ (^ — a) (2).
Let It be the distance of the point of projection from t...he center; /8 the angle, and Fthe velocity, of projection ; then when ^ = 0, «"5' ^«*^=-SSL- Hence, by (1), —^ — 1 = 6 cos a, .and, by (2), ~».^^* )8 = - e sin a.
From these^ tan a= —75 — f!
•(3).
h* ,« 2/* and **=';?^jJ,e>l, and the orbit is a hyperbola, F*=^, e = l, a parabola, F*
What to read after A Treatise On Dynamics of a Particle, With Numerous Examples?
You can find similar books in the "Read Also" column, or choose other free books by Peter Guthrie Tait to read onlineMoreLess
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