The field equations of motion and compatibility for the nonlinear dynamics of doubly curved shells are recast in an intrinsic form, in terms of the metric and curvature functions of their reference surfaces. For appropriate input, the motion of the shell is described without the need for an external reference coordinate system or the use of vector quantities such as position, velocity, and acceleration. The equations are shown to be readily applicable to time integration schemes. Such cases, as the (spatially) constant load problem and the inextensional dynamics problem, are also considered. The need for further work in the area is emphasized.

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