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Full-Text Articles in Physical Sciences and Mathematics
Gravitational Slingshot , John Dykla, Robert Cacioppo, Asim Gangopadhyaya
Gravitational Slingshot , John Dykla, Robert Cacioppo, Asim Gangopadhyaya
Asim Gangopadhyaya
The slingshot effect is an intriguing phenomenon that has been used effectively by NASA to send spacecraft to outer edges of the solar system. This phenomenon can be satisfactorily explained by Newtonian physics. However, if it is presented as a problem involving four-momentum conservation, the methods of relativistic kinematics easily lead to the conditions necessary for an accelerating as well as a retarding scenario. This problem provides an example that showcases the frequent utility of relativistic methods to analyze problems of Newtonian mechanics.
Unintended Consequences Of Imprecise Notation – An Example From Mechanics, Asim Gangopadhyaya, Gordon Ramsey
Unintended Consequences Of Imprecise Notation – An Example From Mechanics, Asim Gangopadhyaya, Gordon Ramsey
Asim Gangopadhyaya
We present a conundrum that results from the imprecise use of notation for partial derivatives. Taking an example from mechanics, we show that lack of proper care in re presenting partial derivatives in Lagrangian and Hamiltonian formulations paradoxically leads to two different values for the time derivative of the canonical momentum. This problem also exists in other areas of physics,such as thermodynamics.