First-order resonant in periodic orbits

In the frame work of Saturn–Titan system, the resonant orbits of first-order are analyzed for three different families of periodic orbits, namely, interior resonant orbits, exterior resonant orbits and [Formula: see text]-Family orbits. This analysis is developed by considering Saturn as a spherical and oblate body. The initial position, semi-major axis, eccentricity, orbital period and order of resonant orbits of these families are investigated for different values of Jacobi constant and oblateness parameter.

Jellyfish Locomotion

Two dichotomies exist within the swim systems of jellyfish—one centered on the mechanics of locomotion and the other on phylogenetic differences in nervous system organization. For example, medusae with prolate body forms use a jet propulsion mechanism, whereas medusae with oblate body forms use a drag-based marginal rowing mechanism. Independent of this dichotomy, the nervous systems of hydromedusae are very different from those of scyphomedusae and cubomedusae. In hydromedusae, marginal nerve rings contain parallel networks of neurons that include the pacemaker network for the control of swim contractions. Sensory structures are similarly distributed around the margin. In scyphomedusae and cubomedusae, the swim pacemakers are restricted to marginal integration centers called rhopalia. These ganglionlike structures house specialized sensory organs. The swim system adaptations of these three classes (Hydrozoa, Scyphozoa, and Cubozoa), which are constrained by phylogenetics, still adhere to the biomechanical efficiencies of the prolate/oblate dichotomy. This speaks to the adaptational abilities of the cnidarian nervous system as specialized in the medusoid forms.

Non-collinear libration points in CR3BP when less massive primary is an heterogeneous oblate body with N-layers

<p>In the present paper, the existence of non-collinear libration points has been shown in circular restricted three-body problem when less massive primary is a heterogeneous oblate body with N-layers. Further, the stability of non-collinear libration points is investigated in linear sense and found that the non-collinear libration points are stable for the critical value of mass parameter <em>µ</em> ≤ <em>µ_crit</em>= <em>µ</em>_o – 3.32792 <em>k</em>₁ – 1.16808 <em>k</em>₂.</p>

Stability of the equilibrium points in the circular restricted four body problem with oblate primary and variable mass

<p>This paper investigates the liberation points and stability of the restricted four body problem with one of the primaries as oblate body and the infinitesimal body is taken as variable mass. Due to oblateness, the equilateral triangular configuration is no longer exists and becomes an isosceles triangular configuration. Moreover, we have found seven equilibrium points out of which three are asymptotically stable (dark black in the tables) and rest four are unstable.</p>