A Treatise On the Analytical Dynamics of Particles And Rigid Bodies With An Int
A Treatise On the Analytical Dynamics of Particles And Rigid Bodies With An Int
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fen 121. Application of the last multiplier to Hamiltonian systems : use of a single known integral.
If the system of differential equations considered is a Hamiltonian system, we have evidently ^dX r /dx r = 0, and consequently M = 1 is a solution of the r partial differential equation which determines the last multiplier ; so the last multiplier of a Hamiltonian system of equations is unity.
From this result we can deduce a theorem which enables us to integrate completely any conservative hol...onomic dynamical system with two degrees of freedom when one integral is known in addition to the integral of energy.
Let the system be ^2i = ^h = dpl dp ~ 2 fit djf d_H _dH _dH dpi dp 2 dqj. Dq 2 and in addition to the integral of energy H (q I} q 2, PI, PZ) h, let an integral V(q l} q 2, pi, pz) = c be known. From the theorem of the last multiplier it follows that 1 (dH, dH = constant 9 (Pi.
120, 121] their Integral- Invariants 281 is another integral ; where, in the integrand, p l and p 2 are supposed to be replaced by their values in terms of q 1 and
What to read after A Treatise On the Analytical Dynamics of Particles And Rigid Bodies With An Int?
You can find similar books in the "Read Also" column, or choose other free books by Whittaker, E. T. (Edmund Taylor), 1873-1956 to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
fen 121. Application of the last multiplier to Hamiltonian systems : use of a single known integral.
If the system of differential equations considered is a Hamiltonian system, we have evidently ^dX r /dx r = 0, and consequently M = 1 is a solution of the r partial differential equation which determines the last multiplier ; so the last multiplier of a Hamiltonian system of equations is unity.
From this result we can deduce a theorem which enables us to integrate completely any conservative hol...onomic dynamical system with two degrees of freedom when one integral is known in addition to the integral of energy.
Let the system be ^2i = ^h = dpl dp ~ 2 fit djf d_H _dH _dH dpi dp 2 dqj. Dq 2 and in addition to the integral of energy H (q I} q 2, PI, PZ) h, let an integral V(q l} q 2, pi, pz) = c be known. From the theorem of the last multiplier it follows that 1 (dH, dH = constant 9 (Pi.
120, 121] their Integral- Invariants 281 is another integral ; where, in the integrand, p l and p 2 are supposed to be replaced by their values in terms of q 1 and
What to read after A Treatise On the Analytical Dynamics of Particles And Rigid Bodies With An Int?
You can find similar books in the "Read Also" column, or choose other free books by Whittaker, E. T. (Edmund Taylor), 1873-1956 to read onlineMoreLess
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