Answer
In the process of muscle contraction, the cross bridges are formed as myosin heads ( with ADP +P) attach to actin binding sites. The next step is the power stroke that opens cross bridges and slide thin filaments towards the center of sarcomeres. For this movement to continue repeating (and the muscle continue contracting) there must be adequate supplies of ATP and Ca++ available to the sarcomere, If there is not enough ATP available, cross bridges cannot be detached from the actin binding sites, and rigidity will set in.
Work Step by Step
Adequate amounts of ATP are necessary to facilitate repetition of the power stroke . This requires release of the myosin head( and ADP+PO4) from the actin binding site. The cross bridges must be rotated to provide the mechanical force to slide the thin filaments towards the interior of the sarcomere. If this sliding process ceases, contraction will be halted, and rigidity will set in.