 | Mathematics - 1908 - 820 pages
...that every force under which a point describes a conic section, whatever be the initial conditions, always passes through a fixed point or remains parallel...of the explicit forms of the forces in the case of conies Stephanos rediscovers the known theorems of Darboux and Halphen.f In the present note free use... | |
 | British Association for the Advancement of Science - Science - 1909 - 1250 pages
...problem admits of no other solution than those included in the case considered by Bertrand, nnd he shows that every force under which a point describes...rediscovers the known results due to Darboux and Halphen. All these discussions have been concerned with the motion of a single material point. Similar problems... | |
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Bertrand, nnd he shows that every force under which a point describes a conic section, whatever be the initial conditions, either always passes through a fixed point or remains parallel to a fixed direction; finally, by applying his method to the determination... 