Conserved Quantities of Lagrange Equation of a Growing Elastic Rod Dynamics

Conservedquantities of a growing elastic roddynamics are studied on the basis of Lagrange equation. Several of conserved quantities and their condition of existencearederived, which expanded the concept of conversation from the time to the space, i.e. arc coordinate.Lagrange equation is applied to analyzed energy integral and cyclic integral. First integrals are of practical significance in both theoretical and numerical analysis for a growing elastic rod dynamics.