The objective of this note is to prove the existence result for brake orbits
in classical Hamiltonian systems (which is first proved by Bolotin) by using
Floer theory. To this end, we compute an open string analogue of symplectic
homology (so called wrapped Floer homology) of some domains in cotangent
bundles, which appear naturally in study of classical Hamiltonian systems. The
main part of the computations is to show invariance of wrapped Floer homology
under certain handle attaching to domains.