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Abstract: In spite of being a classical method for solving differential equations, the method of variation of parameters continues having a great interest in theoretical and practical applications, as in astrodynamics. In this paper we analyse this method providing some modifications and generalised theoretical results. Finally, we present an application to the determination of the ephemeris of an artificial satellite, showing the benefits of the method of variation of parameters for this kind of problems. [Copyright &y& Elsevier]

Abstract: Nonlinear variation of parameters formula for set differential equations in a metric space is developed investigating necessary tools such as differentiability of solutions relative to initial values. Other needed results are also proven. [Copyright &y& Elsevier]