We derive a velocity-dependent potential for describing the dynamics of a rigid body in a rotating frame. We show that, as for one-particle systems, the different components of this potential can be associated with electromagnetic analogs. We provide some examples to demonstrate the feasibility of using the potential as an alternative description of rigid body problems.
REFERENCES
1.
M. D.
Semon
and G. M.
Schmieg
, “Note on the analogy between inertial and electromagnetic forces
,” Am. J. Phys.
49
, 689
–690
(1981
).3.
G. G.
Coriolis
, “Mémoire sur le principe des forces vives dans les mouvements relatifs des machines
,” J. Ec. Polytech. (Paris)
13
, 268
–302
(1832
).4.
G. G.
Coriolis
, “Mémoire sur les équations du mouvement relatif des systèmes de corps
,” J. Ec. Polytech. (Paris)
15
, 142
–154
(1835
).5.
P. S.
Laplace
, “Recherches sur plusieurs points du systeme du monde
,” Memoires de l’Academie Royale des Sciences de Paris
88
, 75
–182
(1776
).6.
C. F.
Hagenow
, “Is there a centrifugal force?
,” Am. Phys. Teach.
3
, 190
(1935
).7.
G. D.
Scott
, “Centrifugal forces and Newton’s laws of motion
,” Am. J. Phys.
25
, 325
(1957
).8.
9.
J.
Sivardiere
, “On the analogy between inertial and electromagnetic forces
,” Eur. J. Phys.
4
, 162
–164
(1983
).10.
E.
Schering
, “Hamilton-Jacobische Theorie für kräfte, deren maass von der bewegung der körper abhängt
,” Abh. Gesellschaft Wiss. Göttingen
18
, 3
–54
(1873
).11.
W.
Weber
, “I. Elektrodynamische Maassbestimmungen
,” Ann. Phys. Chem.
73
, 193
–240
(1848
) [shortened version of the 1846 paper published in the Abhandlungen der Koniglichen Sachsischen Gesellschaft der Wissenschaften, Leipzig].12.
E. T.
Whittaker
, A Treatise on the Analytical Dynamics of Particles and Rigid Bodies
(Cambridge U. P.
, Cambridge
, 1904
).13.
14.
M. L.
Coffman
, “Velocity-dependent potentials for particles moving in given orbits
,” Am. J. Phys.
20
, 195
–199
(1952
).15.
R.
Coisson
, “On the vector potential of Coriolis forces
,” Am. J. Phys.
41
, 585
(1973
).16.
G.
Rousseaux
, “The gauge non-invariance of classical electromagnetism
,” Ann. Fond. Louis Broglie
30
, 387
–396
(2005
).17.
M. B.
May
, “Elmer A. Sperry and the gyrocompass
,” Inst. Navigation Newslet.
17
, 8
–9
(2007
).18.
G. I.
Opat
, “Coriolis and magnetic forces: The gyrocompass and magnetic compass as analogs
,” Am. J. Phys.
58
, 1173
–1176
(1990
).19.
J.
Barcelos-Neto
and M. B.
Dias da Silva
, “An example of motion in a rotating frame
,” Eur. J. Phys.
10
, 305
–308
(1989
).20.
K.
Weltner
, “Stable circular orbits of freely moving balls on rotating discs
,” Am. J. Phys.
47
, 984
–986
(1979
).21.
A. M.
Bloch
, P. S.
Krishnaprasad
, J. E.
Marsden
, and R.
Murray
, “Nonholonomic mechanical systems with symmetry
,” Arch. Ration. Mech. Anal.
136
, 21
–99
(1996
).22.
Lev Elsgoltz,
Differential Equations and Variational Calculus
(MIR
, Moscow
, 1977
).23.
E.
Noether
, “Invariante Variationsprobleme
,” Nachr. Ges. Wiss. Goettingen, Math.-Phys. Kl.
2
, 235
–257
(1918
).24.
E. A.
Desloge
and R. I.
Karch
, “Noether’s theorem in classical mechanics
,” Am. J. Phys.
45
, 336
–339
(1976
).© 2008 American Association of Physics Teachers.
2008
American Association of Physics Teachers
AAPT members receive access to the American Journal of Physics and The Physics Teacher as a member benefit. To learn more about this member benefit and becoming an AAPT member, visit the Joining AAPT page.