Natural SciencesAstronomyPhysicsAstrophysicsDynamical SystemsTheoretical AstronomyGalaxy ClustersStar ClustersStellar AstrophysicsStellar DynamicsStellar PopulationsStellar StructureCluster Relaxation StateDisintegration MechanismsFirst-principles ModelingGalaxy Cluster DynamicsHamiltonian Partial Differential EquationsSpiral Galaxy StructureStar Cluster DynamicsStar Cluster Relaxation Processes