Calculus of variation is one of the oldest yet still continually
developing branches of analysis. Physical variational principles
were discovered prior to the birth of modern calculus and
associated with names such as Fermat. With the historical
development of the differential and integral calculus of
Newton and Leibniz, the principle of extreme action in mechanics was
formulated with effort from Maupertuis, Euler and Lagrange in
mid-eighteenth century, followed by the work of deriving the equations of motion
from the variational principles by Jacobi and Hamilton nearly one
hundred years later. Since then calculus of variation has become one
of the main tools in analysis, with numerous applications in physical
sciences and engineering.
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