The problem of how to optimally traverse a spray applicator around a surface to be coated is formulated as a type of optimization problem known as a constrained variational problem. An optimal trajectory for a spray applicator is defined to be one that results in minimal variation in accumulated film thickness on the surface. The trajectory for an applicator is characterized by a six-dimensional vector function that specifies the position and orientation of the applicator at each instant of time. The surface to be coated is represented with a function. For each surface point and fclr each feasible position and orientation of the applicator, a value for the instantaneous rate of film accumulat'lon is assumed to be known. Empirical data and/or estimates for these values can be readily incorporated in the formulation. By making realistic approximations, the proposed constrained variational problem is transformed into a finite dimensional constrained optimization problem. Numerical studies are included that illustrate the utility of the problem formulation and the effectiveness of applying standard nonlinear programming techniques for determining solutions.
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