This paper presents a rigorous kinematic analysis of the motion of a material point along an elliptical trajectory within a coordinate system aligned with its geometric center. Based on the sequential differentiation of constraint equations in a Cartesian coordinate system, an angular differential equation of motion is derived. It is proved that, in contrast to the focal description (the Kepler problem), the areal velocity of a point moving relative to the center of an ellipse is not a constant value and varies cyclically over time. An analytical expression for the variable angular velocity is obtained, and the equations of motion are integrated, allowing for the precise determination of the polar angle as a function of time. This work complements the classical concepts of theoretical mechanics regarding the connection between the geometry of conic sections and the physics of central force fields.