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Inverted pendulums are important objects of theoretical investigation and experiment in the area of control theory and engineering.The researches concentrate on the rigid finite dimensional models which are described by ordinary differential equations(ODEs).Complete rigidity is the approximation of practical models;Elasticity should be introduced into mathematical models in the analysis of system dynamics and integration of highly precise controller.A new kind of inverted pendulum,elastic inverted pendulum was proposed,and elasticity was considered.Mathematical model was derived from Hamiltonian principle and variational methods,which were formulated by the coupling of partial differential equations(PDE) and ODE.Because of infinite dimensional,system analysis and control of elastic inverted pendulum is more sophisticated than the rigid one.