Continuum mechanics vs Classical mechanics are they the same?

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Discussion Overview

The discussion centers around the relationship and differences between continuum mechanics and classical mechanics, exploring whether a course in continuum mechanics provides the same background as classical mechanics or if both are necessary. The scope includes theoretical distinctions and educational pathways in physics and engineering.

Discussion Character

  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • Some participants suggest that continuum mechanics is primarily a mathematical course, while classical mechanics is rooted in physics, indicating a fundamental difference between the two.
  • One participant argues that continuum mechanics deals with field theory and the mechanics of objects with spatial extent, contrasting it with classical mechanics, which focuses on mass-points.
  • Another participant elaborates that classical mechanics often involves analyzing the dynamics of particles or bodies that behave like particles, while continuum mechanics addresses real objects, such as the deformation of materials under load.
  • Some participants note that many classical mechanics courses provide a limited introduction to continuum mechanics, suggesting an overlap in content but differing emphases.
  • There is a claim that the majority of mechanics work in engineering, particularly in fields like fluid dynamics and solid mechanics, is actually continuum mechanics, which may challenge the characterization of continuum mechanics as merely a mathematical course.
  • A participant mentions that plasma physics, specifically magnetohydrodynamics (MHD), is also considered a part of continuum mechanics, indicating its broader applications.

Areas of Agreement / Disagreement

Participants express differing views on the relationship between continuum mechanics and classical mechanics, with no consensus on whether one can fully substitute for the other in educational contexts.

Contextual Notes

There are limitations in the discussion regarding the definitions of continuum mechanics and classical mechanics, as well as the assumptions made about the content and structure of courses in these areas. The discussion does not resolve the complexities of how these fields interact or the specific prerequisites for studying them.

Eng_physicist
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Will taking a course is continuum mechanics give me the same background as in classical mechanics or would I need to take both separately? Can anyone explain the difference if there is one between classical mechanic vs continuum mechanics in simple nontechnical terms.
 
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Continuum mechanics is math course and classical mechanics is a physics course. So, yes there is a difference, you should probably take classical mechanics before continuum mechanics (it is a graduate level math course at my local university).
 
Eng_physicist said:
Will taking a course is continuum mechanics give me the same background as in classical mechanics or would I need to take both separately? Can anyone explain the difference if there is one between classical mechanic vs continuum mechanics in simple nontechnical terms.

Continuum mechanics is a field theory, while classical mechanics is a theory of mass-points.
 
To elaborate on what Andy is saying, what you spend most of your time doing in courses called "classical mechanics" is to analyze the dynamics of particles or bodies that act like particles (e.g. relative distances between the planets and the sun vs. their diameters makes the analysis particle-like, and similar for the trajectory of an ICBM over a rotating Earth). Some/most physics books (both at the grad and undergrad levels) on classical mechanics will give some sort of (limited) introduction to continuum mechanics though.

So continuum mechanics is the mechanics of "real" objects that have spatial extent. Think of placing a bunch of heavy physics textbooks on a wood bookshelf. Over time, that specific shelf will start to sag; can you calculate how so? Not with particle dynamics!

The first sentence of Post #2 is actually a bit misleading, although sometimes correct. The majority of "mechanics" that a mechanical engineer does is actually continuum mechanics (fluids, deformations of solids, etc.). Furthermore, plasma physics (MHD specifically) is essentially continuum mechanics!

This http://en.wikipedia.org/wiki/Continuum_mechanics#Major_areas_of_continuum_mechanics" actually gives a good synopsis.
 
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