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The (total) normal force, denoted by N (1→2) , is the normal vector component of the resultant of the contact dynam. In other words, we denote: T (1→2) = ∫ t dS , (1-7) N (1→2) = ∫ n dS . (1-8) S S D The rolling moment, about p, denoted M tp , is the tangential part of the moment of contact dynam. The pivoting moment, about p, denoted M np , is the normal part of the moment of contact dynam. 50 Chapter 1 To sum up, we simply denote: L=T + N , (1-9) M p = M tp + M np . (1-10) Remark. The contact between two bodies strictly at a point is an idealized situation; in reality, there is always a contact area.

Dt This vector is sometimes called the velocity vector of q relative to O. It is the derivative of every vector “fixed” in the rigid body B. Remark. The angular velocity ω does not depend on the choice of reference point O. Indeed, given ( dOq ) e = ω ∧ Oq , dt we are going to prove that, for another point of reference O1 : ( dO1q ) e = ω ∧ O1q . dt ( dO1q ) e = ω1 ∧ O1q dt A priori, we have: but ( dO1q dOO1 dOq )e = ( )e − ( ) e = ω ∧ Oq − ω ∧ OO1 dt dt dt = ω ∧ (OO1 + O1q) − ω ∧ OO1 = ω ∧ O1q .

This analytical mechanics method brings into play virtual displacements or virtual velocities (which are arbitrary vectors a priori). In short, statics is concerned with three types of problems, namely: - searching for equilibrium positions of mechanical systems in presence of known forces, looking for forces which insure the equilibrium of system, studying the stability of equilibrium. The classic and “virtual” methods have application fields which are somewhat complementary. So, the classic method is especially used for trying to find forces which maintain material systems in equilibrium.

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Solid Mechanics and Processing [symposium procs]


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