The criteria of \(d\)-\(\delta\) operations' exchange relationship in nonholonomic systems of analytical dynamics (Q1369375)

The authors consider the exchange relationship between differential operation \(d\) and variational operation \(\delta\) as one of the basic problems of analytical mechanics. Taking into account the classical definition of variation, the criteria determining whether the \(d\)-\(\delta\) operations are exchangeable or not are presented for generalized coordinates and velocities which appear explicitly in the nonholonomic constraint equations of motion. Thus, it is shown that the exchange relationship for \(d\)-\(\delta\) operations is not universally tenable.