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The dense cores associated with star formation derive dynamical support from static magnetic fields, thermal motions, and Alfv\'en waves. The stability of such configurations is an important issue, because precollapse conditions in a core affect the infall process and determine whether fragmentation into a multiple star system will occur. A formalism is described to calculate the equilibria and stability criteria associated with a non--rotating, pressure--bounded sphere that is dynamically supported by multiple ideal gas components. Each gas component has independent adiabatic and polytropic exponents, defined by $P\propto\rho^\gamma$. Static magnetic fields and Alfv\'en waves are then incorporated into the stability analysis heuristically. We investigate the circumstances under which the simplicity of this 1-D model can be exploited to shed light on the structure of molecular clouds and the early stages of star formation.
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