Abstract
The 1-D optimum path problem with two end-points fixed or one end-point fixed, the other end-point variable reduces to vector integral equations of Fredhom / Volterra type and is hard to solve. Translating it to scalar components equations would be an easier way of solving it. Here, the solution of the optimum path problem is recommended by connecting it with the Principle of minimum Energy Release (PMER). A lot of optimum path problems with path function E=cu2, where E is the released energy, u is the velocity, c is constant, can be solved by PMER, e.g., the Great Earthquake, the denotation of a nuclear weapon, the strategy of sports games. The one end-point fixed, the other end-point variable is studied for wing moving. High lights: The pulse-mode of nuclear denotation releasing energy is the same as Earthquake, Yun [1], shows that the derivative of wind velocity with respect to time in proportion to the derivative of temperature with respect to the track. Which conforms with the weather forecast in winter that strong wind companies with low temperature for cold wave coming, and also suits for the motion of mushroom cloud [2].
Highlights
There are many 1-D optimum path problems existing in universal and diary life
This paper aims to set up relationship between the 1-D optimum path problem and the “Principle of Minimum
The optimum path problem of 1-D two end-points A and B fixed is reduced to an optimum of an vector integral equation of Fredholm type, i.e
Summary
There are many 1-D (one dimension) optimum path problems existing in universal and diary life. Optimum path in logistics navigation, optimum path in military design-attacking target, optimum path in wind moving track, and typhoon track, etc. The 1-D optimum path problem with constraint(s), usually, it can be changed to un-constraint problem by method of Lagrange multipliers [3]. The optimum problem of integrand with given scalar function have been summery in mathematical hand books, e.g., [4]. There are many principles on energy relating to mechanical problems or relating to scientific problems. These principles have no connection with the optimum path problem
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