Both further developed Lagrange's method and applied it to mechanics, which led to the formulation of Lagrangian mechanics. Lagrange solved this problem in 1755 and sent the solution to Euler. Donald was a 1968 graduate of Woodward High School and married Mary Beth Pomorski on February, 26, 1972. He was born Novemin LaPorte, Indiana to Robert and Vola (LaFever) Euler. This is the problem of determining a curve on which a weighted particle will fall to a fixed point in a fixed amount of time, independent of the starting point. Euler, age 71, of Swanton, Ohio, passed away peacefully in his home, Monday, January 3, 2022. The Euler–Lagrange equation was developed in the 1750s by Euler and Lagrange in connection with their studies of the tautochrone problem. In classical field theory there is an analogous equation to calculate the dynamics of a field. It has the advantage that it takes the same form in any system of generalized coordinates, and it is better suited to generalizations. Its negative resolution by Leonhard Euler in 1736 laid the foundations of graph theory and prefigured the idea of topology. The Seven Bridges of Königsberg is a historically notable problem in mathematics. This is particularly useful when analyzing systems whose force vectors are particularly complicated. Map of Königsberg in Eulers time showing the actual layout of the seven bridges, highlighting the river Pregel and the bridges. In classical mechanics, it is equivalent to Newton's laws of motion indeed, the Euler-Lagrange equations will produce the same equations as Newton's Laws. In this context Euler equations are usually called Lagrange equations. In Lagrangian mechanics, according to Hamilton's principle of stationary action, the evolution of a physical system is described by the solutions to the Euler equation for the action of the system. This is analogous to Fermat's theorem in calculus, stating that at any point where a differentiable function attains a local extremum its derivative is zero. The equations were discovered in the 1750s by Swiss mathematician Leonhard Euler and Italian mathematician Joseph-Louis Lagrange.īecause a differentiable functional is stationary at its local extrema, the Euler–Lagrange equation is useful for solving optimization problems in which, given some functional, one seeks the function minimizing or maximizing it. In the calculus of variations and classical mechanics, the Euler–Lagrange equations are a system of second-order ordinary differential equations whose solutions are stationary points of the given action functional. Second-order partial differential equation describing motion of mechanical system
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