Abstract
The standard classical mechanics textbooks used at graduate level mention geometrization of the potential motion kinematics. We show that the complete problem can also be geometrized, presenting the system of equations of geometric origin equivalent to the equations of motion of the potential system. The subject seems to be an excellent opportunity for introducing differential geometry concepts already in the classical mechanics course. After presenting the necessary differential geometry notions, the classical mechanical potential system is described in geometric terms. To the system one associates a Riemann space with an appropriately chosen metric and affine connection, both specified by the potential. In this picture, both dynamics and kinematics acquire invariant geometric meaning.
| Original language | English |
|---|---|
| Pages (from-to) | 767-780 |
| Number of pages | 14 |
| Journal | European Journal of Physics |
| Volume | 29 |
| Issue number | 4 |
| DOIs | |
| Publication status | Published - 1 Jul 2008 |
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ASJC Scopus subject areas
- Physics and Astronomy(all)
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Potential motion in a geometric setting : Presenting differential geometry methods in a classical mechanics course. / Deriglazov, A. A.
In: European Journal of Physics, Vol. 29, No. 4, 01.07.2008, p. 767-780.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Potential motion in a geometric setting
T2 - Presenting differential geometry methods in a classical mechanics course
AU - Deriglazov, A. A.
PY - 2008/7/1
Y1 - 2008/7/1
N2 - The standard classical mechanics textbooks used at graduate level mention geometrization of the potential motion kinematics. We show that the complete problem can also be geometrized, presenting the system of equations of geometric origin equivalent to the equations of motion of the potential system. The subject seems to be an excellent opportunity for introducing differential geometry concepts already in the classical mechanics course. After presenting the necessary differential geometry notions, the classical mechanical potential system is described in geometric terms. To the system one associates a Riemann space with an appropriately chosen metric and affine connection, both specified by the potential. In this picture, both dynamics and kinematics acquire invariant geometric meaning.
AB - The standard classical mechanics textbooks used at graduate level mention geometrization of the potential motion kinematics. We show that the complete problem can also be geometrized, presenting the system of equations of geometric origin equivalent to the equations of motion of the potential system. The subject seems to be an excellent opportunity for introducing differential geometry concepts already in the classical mechanics course. After presenting the necessary differential geometry notions, the classical mechanical potential system is described in geometric terms. To the system one associates a Riemann space with an appropriately chosen metric and affine connection, both specified by the potential. In this picture, both dynamics and kinematics acquire invariant geometric meaning.
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UR - http://www.scopus.com/inward/citedby.url?scp=46749159316&partnerID=8YFLogxK
U2 - 10.1088/0143-0807/29/4/011
DO - 10.1088/0143-0807/29/4/011
M3 - Article
AN - SCOPUS:46749159316
VL - 29
SP - 767
EP - 780
JO - European Journal of Physics
JF - European Journal of Physics
SN - 0143-0807
IS - 4
ER -