mathematical foundations of mechanics
E494906
The mathematical foundations of mechanics comprise the rigorous principles and equations, rooted in calculus and Newtonian laws, that describe and predict the motion and interaction of physical bodies.
Statements (50)
| Predicate | Object |
|---|---|
| instanceOf |
area of mathematics
ⓘ
subfield of mathematical physics ⓘ theoretical framework ⓘ |
| appliesTo |
continuous media
ⓘ
elastic bodies ⓘ fluids ⓘ point particles ⓘ rigid bodies ⓘ |
| basedOn |
Newton's laws of motion
NERFINISHED
ⓘ
Newtonian mechanics NERFINISHED ⓘ calculus ⓘ differential equations ⓘ differential geometry ⓘ functional analysis ⓘ law of universal gravitation ⓘ linear algebra ⓘ measure theory ⓘ symplectic geometry ⓘ variational calculus ⓘ vector calculus ⓘ |
| fieldOfStudy |
analytical mechanics
ⓘ
classical mechanics ⓘ continuum mechanics ⓘ particle mechanics ⓘ rigid body mechanics ⓘ |
| formalismIncludes |
Hamiltonian mechanics
ⓘ
Hamilton–Jacobi theory NERFINISHED ⓘ Lagrangian mechanics NERFINISHED ⓘ Newtonian formulation ⓘ Noether's theorem NERFINISHED ⓘ Poisson bracket formalism ⓘ canonical transformations ⓘ dynamical systems theory ⓘ principle of least action ⓘ stability theory ⓘ variational principles ⓘ |
| goal |
mathematical consistency of mechanical theories
ⓘ
prediction of mechanical behavior ⓘ rigorous description of motion ⓘ |
| relatedTo |
applied mathematics
ⓘ
engineering mechanics ⓘ mathematical foundations of physics ⓘ |
| studies |
boundary value problems
ⓘ
chaotic behavior in mechanical systems ⓘ conservation laws ⓘ equations of motion ⓘ initial value problems ⓘ integrability of systems ⓘ stability of motion ⓘ symmetries of mechanical systems ⓘ |
Referenced by (1)
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