CONSERVATION LAW OF HAMILTONIAN FUNCTION IN SYMPLECTIC SYSTEM OF POLAR COORDINATE ELASTICITY

With similar form of Hamiltonian function in symplectic system of rectangular coordinate elasticity, the function is defined in both radial and circumferential symplectic system of polar coordinate problems. The conservation property of Hamiltonian function is discussed. The conservation law of Hamiltonian function is deduced from Hamilton's dual equations, and the conservation condition is presented. It is pointed out that whether Hamiltonian function is conservative depends on the loads and displacements on two sides in two symplectic systems of polar coordinate elasticity. Two examples are given to verify the conservation law in radial and circumferential symplectic system. The law is useful in analyzing the polar coordinate elasticity and provides an estimating basis for numerical calculations in this field.