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{{Other uses|Weight distribution}} | |||
In [[physics]] and [[mechanics]], '''mass distribution''' is the spatial distribution of [[mass]] within a [[solid]] body. In principle, it is relevant also for [[gas]]es or [[liquid]]s, but on earth their mass distribution is almost homogeneous. | |||
==Astronomy== | |||
In [[astronomy]] mass distribution has decisive influence on the development e.g. of [[nebula]]e, [[star]]s and [[planet]]s. | |||
The mass distribution of a '''solid''' defines its [[center of gravity]] and influences its dynamical behaviour - e.g. the [[oscillation]]s and eventual [[rotation]]. | |||
==Mathematical modelling== | |||
A mass distribution can be modeled as a [[Measure (mathematics)|measure]]. This allows point masses, line masses, surface masses, as well as masses given by a volume density function. Alternatively the latter can be generalized to a [[distribution (mathematics)|distribution]]. For example, a point mass is represented by a [[Dirac_delta#Generalizations|delta function defined in 3-dimensional space]]. A surface mass on a surface given by the equation ''f(x,y,z)'' = 0 may be represented by a density distribution ''g(x,y,z) δ (f(x,y,z))'', where <math>g/\mid \nabla f \mid</math> is the mass per unit area. | |||
The [[mathematical model]]ling can be done by [[potential theory]], by numerical methods (e.g. a great number of [[point mass|mass point]]s), or by theoretical [[mechanical equilibrium|equilibrium]] figures. | |||
==Geology== | |||
In [[geology]] the aspects of rock [[density]] are involved. | |||
==Rotating solids== | |||
[[Rotation|Rotating]] solids are affected considerably by the mass distribution, either if they are homogeneous or inhomogeneous - see [[Torque]], [[moment of inertia]], [[wikt:wobble|wobble]], [[:wikt:imbalance|imbalance]] and [[stability]].{{Disambiguation needed|date=August 2011}} | |||
==Related topics== | |||
* [[gravity]], [[Initial mass function|mass function]], [[Bouguer plate]], [[critical mass]] | |||
* [[angular momentum]], [[asymmetry]], [[geoid]], [[isostasy]], [[polar motion]] | |||
* [[mass spectrum]], [[molar mass distribution]], [[atmosphere]] | |||
==External links== | |||
* [http://www.geod.uni-bonn.de/apmg/projekte/dfg/schwerpunkt_texte/mass_transport_proposal_spp.pdf Mass distribution of the Earth]{{dead link|date=April 2013}} | |||
[[Category:Mechanics]] | |||
[[Category:Celestial mechanics]] | |||
[[Category:Geophysics]] | |||
[[Category:Mass]] | |||
Latest revision as of 09:10, 14 November 2012
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In physics and mechanics, mass distribution is the spatial distribution of mass within a solid body. In principle, it is relevant also for gases or liquids, but on earth their mass distribution is almost homogeneous.
Astronomy
In astronomy mass distribution has decisive influence on the development e.g. of nebulae, stars and planets. The mass distribution of a solid defines its center of gravity and influences its dynamical behaviour - e.g. the oscillations and eventual rotation.
Mathematical modelling
A mass distribution can be modeled as a measure. This allows point masses, line masses, surface masses, as well as masses given by a volume density function. Alternatively the latter can be generalized to a distribution. For example, a point mass is represented by a delta function defined in 3-dimensional space. A surface mass on a surface given by the equation f(x,y,z) = 0 may be represented by a density distribution g(x,y,z) δ (f(x,y,z)), where is the mass per unit area.
The mathematical modelling can be done by potential theory, by numerical methods (e.g. a great number of mass points), or by theoretical equilibrium figures.
Geology
In geology the aspects of rock density are involved.
Rotating solids
Rotating solids are affected considerably by the mass distribution, either if they are homogeneous or inhomogeneous - see Torque, moment of inertia, wobble, imbalance and stability.Template:Disambiguation needed
Related topics
- gravity, mass function, Bouguer plate, critical mass
- angular momentum, asymmetry, geoid, isostasy, polar motion
- mass spectrum, molar mass distribution, atmosphere