In this paper we consider controlled orbital motion in a neighborhood
of first collinear libration point L1 of Earth-Sun system. Circular
restricted three-body problem is used as a mathematical model.
Also, we use nonlinear Hill’s equations and linearized equations for local
description of orbital motion in a neighborhood of L1. We consider
special formulation of controlled motion and we present family of controls,
which save hamiltonian form of equations of motion. With help
of Hamiltonian we give the estimation of controllability region and of
the charge of necessary control influence.