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The text explains canonical transformations, denoted by qi tilde and pi tilde, as functions of tq and pi. These transformations must satisfy a condition for q and p with respect to q tilde and p tilde to be non-zero. A transformation is considered canonical if it converts one Hamilton system to another, where qi dot = dqi/dt and pi dot = -∂H/∂qi. The transformed system uses qi tilde dot = ∂H/∂pi and pi tilde dot = -∂H/∂qi tilde.