Modern cosmology suggests that galaxies and galaxy clusters formed in gravitational potential wells defined by dark matter overdensities in the structural formation stage of the universe. Therefore, the decomposition of matter into baryonic and dark contributions is a fundamental problem for studies of galaxies. This decomposition is the easiest for the Solar Neighborhood in the entire universe due to the availability of dynamical measurements, for which dynamical equilibrium is often assumed. However, many recent big telescopes and sky surveys have provided evidence against the equilibrium assumption, with the most iconic feature being the spiral patterns of number counts, mean radial velocity and mean azimuthal velocity in the vertical phase space. Under such a context, while baryonic-dark decomposition remains a fundamental problem, understanding the Milky Way’s disequilibrium also becomes important. In this thesis, we developed new algorithms to simultaneously fit the Solar Neighborhood gravitational potential and the stellar distribution in phase spaces. Such simultaneous fittings not only measured the gravitational potential and decomposed them into baryonic and dark contributions, they also made it convenient for residual analysis in arbitrary spaces. Taking this advantage, we adopted the theory of phase mixing after an ancient perturbation for the origin of phase spirals, and analyzed our fitting residuals in frequency-angle spaces accordingly to measure the perturbation age. We first confined our fitting to the vertical dimension and developed a new form of distribution function (DF). Our potential and DF profiles along with the measured perturbation age all agreed well with literature. However, we found that assuming separable in-plane and vertical dynamics of the Solar Neighborhood caused disagreement between fitting results for stellar populations with different extent of radial motions. Therefore, we proceeded to work in the entire 6D phase space, assuming global Milky Way potential models and disk DF models. We found that although the potential measurements still agreed with the literature, the difference of potential and force measurements between different choices of models were far beyond individual statistical uncertainties. We also found patterns of fitting residuals in frequency-angle spaces that suggested more complicated origins of the vertical phase spirals than a single ancient perturbation event. The complexity of dynamical history of the Milky Way disk was also suggested by many other simulations while we worked on the baryonic-dark decomposition and the perturbation age measurement. To better understand the response of the stellar disk to external perturbations, we conduct preliminary axisymmetric simulations of the interaction of a satellite and a disk galaxy, and find a variety of outwards propagating waves and also the formation of the vertical phase spirals. We derive moment equations for the disk waves and analyze their evolution during the disk-satellite interaction. We also derive moment equations for the vertical phase spirals and discuss their possible applications in future studies.