Consider again the system studied in Example 4.2. Suppose the integrals ϕ = ϕ(t) and ξ = ξ(t) of the equations of motion are known; find the constraint reactions φ1 and φ2 on the two points of the...

Consider again the system studied in Example 4.2. Suppose the integrals ϕ = ϕ(t) and ξ = ξ(t) of the equations of motion are known; find the constraint reactions φ1 and φ2 on the two points of the system. In this particular case, the problem is simple; indeed, once the accelerations a1, a2 are known, it is enough to write φi = miai − Fi. However, it is useful to illustrate the general procedure. We start by computing the unit base vectors of the normal space, writing the constraint equation in the form (see Fig. 4.1) 2f1 = x2 1 + y2 1 − R2 = 0, f2 = y1x2 − x1y2 = 0, and hence ∇f1 = (x1, y1, 0, 0), ∇f2 = (−y2, x2, y1, −x1).