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We derive a variational principle for the dynamical stability of a cluster asa gas sphere in a box. Newtonian clusters are always dynamically stable and,for relativistic clusters, the relation between dynamical and thermodynamicalinstabilities is analyzed. The boundaries between dynamically andthermodynamically stable and unstable models are found numerically forrelativistic stellar systems with different cut off parameters. A criterionbased on binding energy curve is used for determination of the boundary ofdynamical stability.Comment: 10 figure

Self‐Gravitating Gas Spheres in a Box and Relativistic Clusters: Relation between Dynamical and Thermodynamical Stability