Parabolic trajectory

Summary

In astrodynamics or celestial mechanics a parabolic trajectory is a Kepler orbit with the eccentricity equal to 1 and is an unbound orbit that is exactly on the border between elliptical and hyperbolic. When moving away from the source it is called an escape orbit, otherwise a capture orbit. It is also sometimes referred to as a C3 = 0 orbit (see Characteristic energy). Under standard assumptions a body traveling along an escape orbit will coast along a parabolic trajectory to infinity, with velocity relative to the central body tending to zero, and therefore will never return. Parabolic trajectories are minimum-energy escape trajectories, separating positive-energy hyperbolic trajectories from negative-energy elliptic orbits. Velocity The orbital velocity (v) of a body travelling along parabolic trajectory can be computed as: :v = \sqrt{2\mu \over r} where: *r is the radial distance of orbiting body from central body, *

Official source

https://en.wikipedia.org/wiki/Parabolic_trajectory

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In this thesis we describe a strategy to control robotic knees and ankles. A dynamical system is used to generate a position trajectory to control a servo motor replacing the missing joint. The dynamical system consists in a pool of coupled oscillators modeling a central pattern generator (CPG). As a first step, anthropometric trajectories of the knee and ankle are learned by the system through the convergence of the oscillators to the specific frequencies, corresponding amplitudes and phase relations. The same system is then used to play back these trajectories. As a sensory feedback to trigger the playback we use one adaptive frequency oscillator to synchronized with the acceleration from the thigh. We use a bipedal model in a physics-based robot simulation environment to test the proposed system. Finally we present a simple hardware implementation of this system on the Agonist-Antagonist Active Knee prototype.

2010

Adaptive fast open-loop maneuvers for quadrocopters

We present a conceptually and computationally lightweight method for the design and iterative learning of fast maneuvers for quadrocopters. We use first-principles, reduced-order models and we do not require nor make an attempt to follow a specific state trajectory-only the initial and the final states of the vehicle are taken into account. We evaluate the adaptation scheme through experiments on quadrocopters in the ETH Flying Machine Arena that perform multi-flips and other high-performance maneuvers.

Springer Verlag2012

Recent advances in trajectory inference from single-cell omics data

Bart Deplancke, Wouter Saelens

Trajectory inference methods have emerged as a novel class of single-cell bioinformatics tools to study cellular dynamics at unprecedented resolution. Initial development focused on adapting methods based on clustering or graph traversal, but recent advances extend the field in different directions. A first class of methods includes novel probabilistic methods that report uncertainties about their outputs, and new methods that consider complementary knowledge, such as unspliced mRNA, time point information, or other types of omics data to construct the trajectory. A second class of methods uses the obtained trajectories as a starting point for novel analyses, such as visualization approaches, new types of statistical analyses, and the possibility to render static analyses more dynamic, such as dynamic gene regulatory network inference.

ELSEVIER2021