Vol.2, No 9, 1999 pp. 843-846
UDC: 531

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THE PRINCIPLE OF ACTION
V.A. Vujičić
Mathematical institute SANU, 11001 Beograd, P.O.Box 367, Yugoslavia

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Abstract. The most common expression for action in physics and mechanics now is ? , where L is Lagrange's function, and for integral variational principle the relation delta J = 0. We define action as the functional  Adt, where A is the work of the forces along real path and emphasize clear difference between elementary work dA = X dx of forces X, X element Rⁿ⁺¹, along real displacement and elementary work delta A = X delta x of the same forces on possible variations of coordinates x, x ? Mn+1. We define the principle of acton by the relation
   ?,
where A(X) is the work of all forces X and A(I) is the work of the force of intertia I and show that known variational principles of mechanics are corollaries of the relation (W).

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PRINCIP DEJSTVA Za pojam dejstva u fizici i mehanici najčešće se uzima integral   ?, gde je L Lagranžova funkcija, a za integralni varijacioni princip uzima se relacija delta J = 0.
Ovde se definiše dejstvo sila kao funkcional Adt , gde je A rad sila duž stvarnog puta; ističe se jasna razlika između elementarnog rada dA = Xdx sila X duž stvarnog pomeranja dx i elementarnog rada tih sila na mogućim varijacijama delta x.
Princip dejstva sila, ili prosto princip dejstva iskazuje se relacijom
 ? ,
gde je A(X) rad sila X i A(I) rad sila inercije I; pokazuje se da se poznati integralni varijacioni principi klasične mehanike javljaju kao posledice ovako ustanovljenog principa.