Abstract
Lagrange's equations are a well known tool for establishing equations of motion of discrete systems. Kinetic energy, which plays a central role in their use, has to be formulated with respect to an inertial system. Lagrange's equations can be formulated favorably with respect to a moving coordinate system as well (e.g. for mechanical systems which themselves are on a moving base), in that the relative kinetic energy is employed. This enables one to get better insight into various inertia forces. The theory revisited is applied to a point mass vibrating on a rotating base.
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References
1.
Shabana
A. A.
, Theory of Vibration, Vol. II: Discrete and Continuous Systems (Springer , New York , 1991 ).
2.
Thomson
W. T.
, Theory of Vibration with Applications , 3rd edn (Unwin Hyman , London , 1989 ).
3.
Craig
R. R.
Jr
, Structural Dynamics (John Wiley , New York , 1981 ).
4.
Benaroya
H.
, Mechanical Vibration (Prentice—Hall , New Jersey , 1998 ).
5.
Marion
J. B.
and
Thornton
S. T.
, Classical Dynamics of Particles and Systems , 4th edn (Saunders College Publishing , Philedelphia , 1995 ).
6.
Tongue
B. H.
, Principles of Vibration (Oxford University Press , New York , 1996 ).
7.
Chow
T. L.
, Classical Mechanics (John Wiley , New York , 1995 ).
8.
McCalion
H.
, Vibration of Linear Mechanical Systems (Longman , London , 1973 ).
9.
Pestel
E.
, Technische Mechanik, Band 3: Kinematik and Kinetik (B. I. Wissenschaftsverlag , Mannheim , 1988 ).
10.
Geradin
M.
and
Rixen
D.
, Mechanical Vibrations: Theory and Application to Structural Dynamics (John Wiley , Chichester , 1994 ).
11.
Lanczos
C.
, The Variational Principles of Mechanics , 4th edn (University of Toronto Press , Toronto , 1970 ).
12.
Baruh
H.
, Analytical Dynamics (McGraw—Hill , Boston , 1999 ).
13.
Meirovitch
L.
, Methods of Analytical Dynamics (McGraw—Hill , New York , 1970 ).
14.
Meirovitch
L.
, Computational Methods in Structural Dynamics (Sijthoff and Nordhoff , Alphen aan den Rijn , 1980 ).
15.
Chetaev
N. G.
, Theoretical Mechanics (Mir Publishers , Moscow ; Springer , Berlin , 1989 ).