Cardiac output is calculated from the area of the concentration curve using the Stewart-Hamilton equation.
2.
They are solutions of the associated Hamilton equations, with ( pseudo-) Riemannian metric taken as Hamiltonian.
3.
This quantity is canonically conjugate to a variable which, by the Hamilton equations of motion changes with time as the gradient of energy with.
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In 1997, he published a generic solution of the Darwin-Hamilton equations that provide an approximative description of multiple Bragg reflection by a mosaic crystal.
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The full set thus has the advantages of both sets of equations, with the convenience of splitting one set of coordinates to the Hamilton equations, and the rest to the Lagrangian equations.
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The time-derivative of " q " is the velocity, and so the second Hamilton equation means that the particle s velocity equals the derivative of its kinetic energy with respect to its momentum.
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Similar theorems have been discovered in other fields, and in physiology it was earlier known as one of the Stewart-Hamilton equations ( e . g . used for estimation of blood volume of organs ).
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In this example, the time-derivative of the momentum " p " equals the " Newtonian force ", and so the first Hamilton equation means that the force equals the negative gradient of potential energy.
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Alternatively, we can argue that these operators must commute if we are to obtain the correct equations of motion from the Hamiltonian, just as the corresponding Poisson brackets in classical theory must vanish in order to generate the correct Hamilton equations.
10.
In the same way the Hamilton equations allow one to derive the time evolution of a system from a set of differential equations, the symplectic form should allow one to obtain a vector field describing the flow of the system from the differential " dH " of a Hamiltonian function " H ".
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