Non-Statistical Factors Present in Successful NBA Rookies

Becoming a successful NBA rookie is a desire of many. Athletes want to be them and coaches and GM’s want to know how to predict them. What non-statistical factors are present in successful NBA rookies? This research used secondary data to show non-statistical factors that were present in successful rookies and what kind of similarities they had. They included, conference, institution, coaching, and draft position, etc... It is important to know what a successful rookie is and if there is a correlation between draft position and rookie success. The point of this research is to show the journeys that the successful rookies took before becoming successful rookies to help better understand what it takes to become a successful rookie

Analysis and control of displaced periodic orbits in the Earth-Moon system

We consider displaced periodic orbits at linear order in the circular restricted Earth-Moon system, where the third massless body is a solar sail. These highly non-Keplerian orbits are achieved using an extremely small sail acceleration. In this paper we will use solar sail propulsion to provide station-keeping at periodic orbits above the L2 point. We start by generating a reference trajectory about the libration points. By introducing a first-order approximation, periodic orbits are derived analytically at linear order. These approximate analytical solutions are utilized in a numerical search to determine displaced periodic orbits in the full nonlinear model. Because of the instability of the collinear libration points, orbit control is needed for a spacecraft to remian in the vicinity of these points. The reference trajectory is then tracked using a linear Quadratic Regulator (LQR). Finally, simulations are given to validate the control strategy. The importance of finding such displaced orbits is to obtain continuous communications between the equatorial regions of the Earth and the polar regions of the Moon

On the stability of displaced two-body lunar orbits

In a prior study, a methodology was developed for computing approximate large displaced orbits in the Earth-Moon circular restricted three-body problem (CRTBP)by the Moon-Sail two-body problem. It was found that far from the L1 and L2 points, the approximate two-body analysis for large accelerations matches well with the dynamics of displaced orbits in relation to the three-body problem. In the present study, the linear stability characteristics of the families of approximate periodic orbits are investigated

Reconfiguring smart structures using approximate heteroclinic connections

A new method is investigated to reconfigure smart structures using the technique of polynomial series to approximate a true heteroclinic connection between unstable equilibria in a smart structure model. We explore the use of polynomials of varying order to first approximate the heteroclinic connection between two equal-energy, unstable equilibrium points, and then develop an inverse method to control the dynamics of the system to track the reference polynomial trajectory. It is found that high-order polynomials can provide a good approximation to heteroclinic connections and provide an efficient means of generating such trajectories. The method is used first in a simple smart structure model to illustrate the method and is then extended to a more complex model where the numerical generation of true heteroclinic connections is difficult. It is envisaged that being computationally efficient, the method could form the basis for real-time reconfiguration of smart structures using heteroclinic connections between equal-energy, unstable configurations

Displaced solar sail orbits : dynamics and applications

We consider displaced periodic orbits at linear order in the circular restricted Earth-Moon system, where the third massless body is a solar sail. These highly non-Keplerian orbits are achieved using an extremely small sail acceleration. Prior results have been developed by using an optimal choice of the sail pitch angle, which maximises the out-of-plane displacement. In this paper we will use solar sail propulsion to provide station-keeping at periodic orbits around the libration points using small variations in the sail's orientation. By introducing a first-order approximation, periodic orbits are derived analytically at linear order. These approximate analytical solutions are utilized in a numerical search to determine displaced periodic orbits in the full nonlinear model. Applications include continuous line-of-sight communications with the lunar poles

Wavelike patterns in precessing elliptical rings for swarming systems

A continuum model for a swarm of devices is investigated with the devices moving along precessing elliptical Earth-centered orbits. Wavelike patterns in these precessing elliptical rings with peaks in swarm density are found that can be used to provide enhanced coverage for Earth observation and space science. Two orbital models are considered for the purpose of comparison: perturbed by J2J2 and solar radiation pressure, and perturbed by J2J2 and J3J3, respectively, each with a different frozen eccentricity. By removing osculating orbital elements, only the long-period orbit eccentricity and argument of perigee are chosen to derive closed-form solutions to the continuum model for the swarm density. Zero-density lines in the swarm density are found, as well as infinite density at certain boundaries. Comparison between the analytic and numerical number density evolutions is made to yield the range of applicable eccentricity based on the maximum error tolerance, as well as the minimum number of swarm members required to approximate continuous evolution. Closed-form solutions are then derived to predict the number density of swarm devices for magnetic-tail measurement and Earth-observation applications

Solar sail trajectories at the Earth-Moon Lagrange points

Paper presented during Session 3, Orbital Dynamics, Symposium C1, Astrodynamics, Paper Number 13. This paper investigates displaced periodic orbits at linear order in the circular restricted Earth-Moon system, where the third massless body is a solar sail. These highly non-Keplerian orbits are achieved using an extremely small sail acceleration. The solar sail Earth-Moon system differs greatly from the Earth-Sun system as the Sun line direction varies continuously in the rotating frame and the equations of motion of the sail are given by a set of nonlinear non-autonomous ordinary differential equations. By introducing a first-order approximation, periodic orbits are derived analytically at linear order. These approximate analytical solutions are utilized in a numerical search to determine displaced periodic orbits in the full nonlinear model. The importance of finding such displaced orbits is to obtain continuous communications between the equatorial regions of the Earth and the polar regions of the Moon. As will be shown, displaced periodic orbits exist at all Lagrange points at linear order