The essential property and developmental course of Euclidean space, symplectic space and bogus symplectic space are studied.

It shows further that solution of the special paradox in classical elasticity is just Jordan canonical form solutions in symplectic space under Hamiltonian system.

Based on the dual variables, the Hamiltonian system theory is introduced into plane orthotropy elasticity, the transformation from Euclidian space to symplectic space is realized.