What is Lagrangian and Hamiltonian mechanics?
Lagrangian exists as the difference between kinetic and potential energy.
Lagrangian is found by the Italian mathematician in the year 1788.
Lagrangian represented by cartesian coordinates.
Hamiltonian is the mathematically sophisticated formulation of classical mechanics.What are the notes on Hamilton's principle?
BASIC PRINCIPLES
This theorem states that the total kinetic energy of a rigid body of mass M is the kinetic energy of a particle of mass M that moves with the center of gravity of the body, plus the kinetic energy of the motion relative to the center of gravity of the body (as if it were fixed).What is Hamilton's equations in classical mechanics?
Now the kinetic energy of a system is given by T=12∑ipi˙qi (for example, 12mνν), and the hamiltonian (Equation 14.3. 6) is defined as H=∑ipi˙qi−L.
For a conservative system, L=T−V, and hence, for a conservative system, H=T+V.- The Lagrangian L is defined as L = T − V, where T is the kinetic energy and V the potential energy of the system in question.
Generally speaking, the potential energy of a system depends on the coordinates of all its particles; this may be written as V = V(x 1, y 1, z 1, x 2, y 2, z 2, . . . ).
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