The article gives a concise description of Hamiltonian dynamics and thermal averages of semiflexible molecules in Cartesian coordinates. Using the concept of constrained inverse matrices introduced by Bott and Duffin [Trans. Am. Math. Soc. 74, 99 (1953)] explicit expressions are derived for the constrained Hamiltonian, the corresponding equations of motion, and the momentum partition function. In this context Fixman-type corrections of constrained configurational averages are derived for different forms of the constraints. It is shown that the use of mass-weighted coordinates leads to a nonbiased sampling of constrained configurational averages in Cartesian coordinates. The formalism allows moreover to define and to calculate effective masses arising in thermal velocity averages of atoms in semiflexible molecules. These effective masses are identical to the corresponding Sachs-Teller recoil masses, which are here generalized to the case of only partially rigid molecules.