We study the dynamics of particles in closed orbits in a galactic disk perturbed by a lopsided halo potential. The underlying potential in a large fraction of spiral galaxies is now believed to have this form. The orbits are solved via first-order epicyclic theory, and the azimuthal variation in the effective surface density is obtained for an exponential disk. The results are obtained first for a flat rotation curve and then for a general power-law rotation curve. These are shown to be valid for both stars and gas in the inner (optical) region of a galaxy because both respond to the same lopsided potential and have comparable disk scale lengths. The results are applied to external lopsided galaxies. An orbit is shown to be elongated along the minimum in the lopsided potential. The net rotational velocity is highest at the minimum radial extent of the orbit. The perturbation parameter for the lop-sided potential epsilon(lop), is obtained as a function of the observed fractional amplitude of the m = 1 azimuthal Fourier component of the surface brightness and the radius. The ellipticity of isophotes is shown to be higher by at least a factor of 4 compared to epsilon(lop). This explains why the phenomenon of lopsidedness is so commonly detected. It also means that even visually strongly lopsided galaxies have a fairly axisymmetric potential, with a small epsilon(lop) < 0.1. The effective disk surface density is highest along the maximum in the lopsided potential, and there is an underdense region in the opposite direction. The maximum increase in the surface density is high similar to 35%-50%, for strongly lopsided galaxies. We obtain the local stability parameter Q(lop) in a lopsided galaxy and show that its values for gas are significantly lowered compared to the axisymmetric case in the overdense region. This is argued to result in an enhanced formation of massive stars which then result in H II regions. Thus we can naturally explain the observed azimuthal asymmetry in the distribution of molecular hydrogen gas and H II regions in the lopsided galaxies such as M101.
