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The dynamic motion of a solder droplet during assembly is a complex, unsteady, free surface problem involving surface tension and viscous effects. The motion of the droplet is coupled with the motion of the component or chip to be assembled and involves dynamic contact lines. A methodology based on a non-uniform rational b-spline (NURBS) discretization has been developed for the dynamic analysis of the droplet motion. A surface energy based formulation has been developed to incorporate the surface tension effects. The developed methodology leads to an updated Lagrangian scheme with a Galerkin in space and Least square in time formulation. The NURBS representation used for the spatial discretization enables the method to handle problems involving complex droplet geometries. The ability of the NURBS representation to provide both global and local control, along with the least square method used in this methodology, enables us to develop an unconditionally stable time integration scheme which can be optimized to achieve desired accuracy and numerical dissipation efficiently. A sample problem of droplet shape evolution has been solved to demonstrate the path prediction capability of the proposed methodology. In future, the method can be applied to solve various real world dynamic motion problems associated with droplets.