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The Timeline History of the Developmeny of
Minimum Principles of Physical Dynamics
In the 2nd century BCE Hero of Alexandria noted that the laws of the reflection of light\
can be derived from the principle that light always takes the shortest path. This principle
does mot explain rhe the laws of the refraction of light.
In 1657 Pierre de Fermat formulated the Principle of Least Time; i.e., that light travels from its initial point to its final point
through reflection and refraction through media in which light travels at different speeds
by folowing the path requiring the least time.
In 1747 Pierre Maupertuis asseted the Principle of Least Action. Action is defined as the a variable having
the same dimensions as length times momentum or energy times time.
Maupertuis asserted that the motion of a physical system takes place in
a way to minimize action. Maupertuis did not give any basis for this principle
other than the theological one that it is God's Wisdom. han a theological one of God's wisdom.
In 1760 the Italian mathematician who adopted the French name of Joseph-Louis Lagrange
gave a mathematically rational basis for
the Principle of Least Action.
In 1828 Carl-Friedrich Gauss formulated the Principle of Least Constraint.
Gauss tried to incorporate the matter of
constraints on motion into the principles of physical dynamics.
In 1834-35 William Rowan Hamiltonian formulated the principle that the path taken by a physical system
is the one which minimizes the integral of the difference
between kinetic and potential energy.
between the kinetic and potential energy came to be known as the Lagrangian of a system.