This thesis studies a process by which a star cluster could migrate to its current position while its stellar members maintain their stable orbits by surfing the stable Lagrange points of a growing and slowing bar. NGC 6791 is a massive metal-rich open cluster in the Milky Way located within the solar circle. Its current mass is measured to be of order magnitude 1,000 solar masses. The age of the cluster is estimated to be approximately 8 Gyr old. Despite experiencing evaporation and tidal shocks, this cluster still exists defying expectations of its impending dissolution. With this purpose, a suite of tracer particle simulations are created to explore the orbits of stars placed at the stable Lagrange point using galpy. Findings showed that 95% of the stellar members stayed within approximately 5.5 pc of the cluster, when the cluster resides at a stable Lagrange point. This work found orbits of a star cluster remain bound together while residing at a bar resonance in the presence of a slowing bar. Bar induced migration is a method that could preserve the stability of orbits in star clusters resulting in a cluster migrating to its current position without dissolving. Adding a vertical component to the position of the cluster could give insight into how vertical oscillations provide an additional factor of binding that could help the cluster stay bound as it migrates to its current location.
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