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Dynamics and Simulation of Flexible Rockets provides a full state, multiaxis treatment of launch vehicle flight mechanics and provides the state equations in a format that can be readily coded into a simulation environment. Various forms of the mass matrix for the vehicle dynamics are presented. The book also discusses important forms of coupling, such as between the nozzle motions and the flexible body. This book is designed to help practicing aerospace engineers create simulations that can accurately verify that a space launch vehicle will successfully perform its mission. Much of the open literature on rocket dynamics is based on analysis techniques developed during the Apollo program of the 1960s. Since that time, large-scale computational analysis techniques and improved methods for generating Finite Element Models (FEMs) have been developed. The art of the problem is to combine the FEM with dynamic models of separate elements such as sloshing fuel and moveable engine nozzles. The pitfalls that may occur when making this marriage are examined in detail. Covers everything the dynamics and control engineer needs to analyze or improve the design of flexible launch vehicles Provides derivations using Lagrange’s equation and Newton/Euler approaches, allowing the reader to assess the importance of nonlinear terms Details the development of linear models and introduces frequency-domain stability analysis techniques Presents practical methods for transitioning between finite element models, incorporating actuator dynamics, and developing a preliminary flight control design

Arun K. Banerjee is one of the foremost experts in the world on the subject of flexible multibody dynamics. This book describes how to build mathermatical models of multibody systems with elastic components. Examples of such systems include the human body itself, construction cranes, cares with trailers, helicopers, spacecraft deploying antennas, tethered satellites, and underwater maneuvering vehicles. This book provides methods of analysis of complex mechanical systems that can be simulated in less computer time than other methods. It equips the reader with knowledge of algorithms that provide accurate results in reduced simulation time.

This book offers a unified presentation that does not discriminate between atmospheric and space flight. It demonstrates that the two disciplines have evolved from the same set of physical principles and introduces a broad range of critical concepts in an accessible, yet mathematically rigorous presentation. The book presents many MATLAB and Simulink-based numerical examples and real-world simulations. Replete with illustrations, end-of-chapter exercises, and selected solutions, the work is primarily useful as a textbook for advanced undergraduate and beginning graduate-level students.

As launch vehicle designs become more slender, the effects of bending vibration on control system stability could be dominant in control systems designed using rigid-body dynamics. Vibrational loads can also cause major damage to the launch vehicle, either in the form of vibrational fatigue or excitation of the structures resonant frequencies. This work investigates a novel method to control vibrations in real time using a real time control target with distributed strain measurements from FBG sensor arrays. Active control of the flexible structure will reduce vibration, which will decrease the chance of damaging the structure. A scaled test article representative of the structural dynamics associated with a slender launch vehicle is designed and built. Finite element analysis modeling methodology is developed to capture the most significant features of test specimen. A model for the entire test article is developed, including frequency response of the cantilever beam, thruster dynamics, and sensor conversion matrices. This research develops, models and provides experimental validation of the use of an array of cold gas thrusters for the real time control of the bending dynamics of a test article. Three separate control algorithms are developed to minimize vibration in the test article, using the FBG strain measurements to calculate required thrust. A classical control algorithm for benchmark purposes, a robust control algorithm and an adaptive control algorithm are implemented. The controller performance is investigated by simulation using the developed model, and these results are experimentally verified using the experimental setup. The performance comparison shows that classic controller is hard to implement experimentally due to decoupling issues, the robust controller achieves good vibration suppression in both simulations and experimental results, and the adaptive controller shows good results, with a potential to surpass the robust controller results in future research. Using the robust controller to control the continuous excited first and second resonant mode of the test setup, shows 94% and 80% reduction of peak-peak vibration respectively, when compared to the open loop response. This research also investigates using the same FBG sensor arrays to reduce the number of IMU sensing units in the launch vehicle.

Volume is indexed by Thomson Reuters CPCI-S (WoS). The collection includes selected peer-reviewed papers from the 2012 International conference on Mechanics , Dynamic Systems and Material Engineering (MDSME2012) held November 24-25, 2012 in Guangzhou, China. The 70 papers are grouped into the following chapters: Chapter 1: Research on Mechanics and Dynamics of Systems in Mechanical Engineering, Chapter 2: Research on Material Engineering and Material Applications.

TRANSFER MATRIX METHOD FOR MULTIBODY SYSTEMS: THEORY AND APPLICATIONS Xiaoting Rui, Guoping Wang and Jianshu Zhang - Nanjing University of Science and Technology, China Featuring a new method of multibody system dynamics, this book introduces the transfer matrix method systematically for the first time. First developed by the lead author and his research team, this method has found numerous engineering and technological applications. Readers are first introduced to fundamental concepts like the body dynamics equation, augmented operator and augmented eigenvector before going in depth into precision analysis and computations of eigenvalue problems as well as dynamic responses. The book also covers a combination of mixed methods and practical applications in multiple rocket launch systems, self-propelled artillery as well as launch dynamics of on-ship weaponry. • Comprehensively introduces a new method of analyzing multibody dynamics for engineers • Provides a logical development of the transfer matrix method as applied to the dynamics of multibody systems that consist of interconnected bodies • Features varied applications in weaponry, aeronautics, astronautics, vehicles and robotics Written by an internationally renowned author and research team with many years' experience in multibody systems Transfer Matrix Method of Multibody System and Its Applications is an advanced level text for researchers and engineers in mechanical system dynamics. It is a comprehensive reference for advanced students and researchers in the related fields of aerospace, vehicle, robotics and weaponry engineering.

Contents: Simulation program for aeroballistic research and trajectory analysis, A simplified ballistics model for sounding rockets, The dynamic equations of a flexible rocket vehicle, Pitch-plane natural frequencies of a flexible sounding rocket, The Aerobee 150 as a ballistic model, Operational requirements of the athena ballistic model, Wind variability over a complex surface, An automatic data collection and processing network, Methods used by the ballistic research laboratories in determining performance parameters for fin stabilized free-flight missiles, recent changes in the analogue data handling capabilities at data analysis center, comparative analysis of various methods of impact point prediction for unguided rockets, circular probable error estimates derivable from one formula, Techniques leading to the formulations of the data report of the meteorological rocket network firings, A general impact prediction scheme for use on a small or medium size computer, A digital computer subroutine for the automatic selection of radar data for instantaneous impact prediction, Development of a ballistic missile target, Some applications of wind to unguided rocket impact predictions, basic requirements for firing unguided rockets relative to missile flight, Basic considerations in the development of an unguided rocket trajectory simulation model, Meteorological instrumentation for rocket ballistic support, Layer wind measurement by acoustic means, Ballistic wind variability, Requirements for field impact predictions, Iterative techniques for computing launcher settings.

"This book describes how to build mathematical models of multibody systems with elastic components. Examples of such systems are the human body itself, construction cranes, cars with trailers, helicopters, spacecraft deploying antennas, tethered satellites, and underwater maneuvering vehicles looking for mines while being connected by a cable to a ship"--

Missiles and launch vehicles are typically slender in shape to reduce aerodynamic drag. Bending vibration of the rocket body occurs when a flying object with a large slenderness ratio actuates the aerodynamic control surfaces to perform pitch or yaw commands. The Inertial Measurement Unit (IMU) onboard the rocket measures the attitude and angular velocities of the deflected body as well as the rigid body motion, and in turn feeds these signals back into the control loop. Feedback of vibrating information usually degrades the control system stability and in the worst cases makes the rocket system unstable. These effects become more significant as the slenderness ratio of the rocket increases. Another important challenge in launch vehicle simulation and control is created by the time-varying mass and inertia of the vehicle, as well as the consequent changes in modal frequencies and modal shapes of the structure as propellant is exhausted. To stabilize the trajectory of a rocket while considering its flexible dynamics, the estimation of displacement, rate of rotation and acceleration at any point on launch vehicle is a critical aspect of mission planning and controller design. The primary objective of this study is to propose a novel model to demonstrate equivalent performance between the Fiber Optic Sensor Array System combined with Forward Navigation IMU (FOSS-IMU System) compared to the standard launch vehicle body bending sensor configuration, as shown in Figure 0-1. The FOSS-IMU system is an innovative algorithm that enables accurate prediction of deflection, rate of rotation and acceleration of any point in the flexible structure relative to the rigid body frame. The FOSS-IMU algorithm is based on modal matrices {[M], [k], [phi], [theta]} that are calculated using only a finite element model of the structure. More importantly, the FOSS-IMU system is based on direct measurements of deflection in multiple points in the structure, which allows accurate estimation of the states of the flexible structure with NO NEED of estimation of load forces or a damping matrix, or no need to assume that the damping is linear and viscous, as current structural models of flexible structures are forced to assume. An experimental benchmark matrix is designed to assess the performance of the proposed system. For each test case FOM (Figure of Merit) Tables are generated to show how well the estimate from FOSS-IMU system compares with raw output from the real IMUs, including the corresponding transformations of reference frames. This study was supported and funded by NASA Launch Services Program based in Kennedy Space Center located in Cape Canaveral, Florida.

This book deals with the problem of dynamics of bodies with time-variable mass and moment of inertia. Mass addition and mass separation from the body are treated. Both aspects of mass variation, continual and discontinual, are considered. Dynamic properties of the body are obtained applying principles of classical dynamics and also analytical mechanics. Advantages and disadvantages of both approaches are discussed. Dynamics of constant body is adopted, and the characteristics of the mass variation of the body is included. Special attention is given to the influence of the reactive force and the reactive torque. The vibration of the body with variable mass is presented. One and two degrees of freedom oscillators with variable mass are discussed. Rotors and the Van der Pol oscillator with variable mass are displayed. The chaotic motion of bodies with variable mass is discussed too. To support learning, some solved practical problems are included.

The book presents up-to-date and unifying formulations for treating dynamics of different types of mechanical systems with variable mass. The starting point is overview of the continuum mechanics relations of balance and jump for open systems from which extended Lagrange and Hamiltonian formulations are derived. Corresponding approaches are stated at the level of analytical mechanics with emphasis on systems with a position-dependent mass and at the level of structural mechanics. Special emphasis is laid upon axially moving structures like belts and chains and on pipes with an axial flow of fluid. Constitutive relations in the dynamics of systems with variable mass are studied with particular reference to modeling of multi-component mixtures. The dynamics of machines with a variable mass are treated in detail and conservation laws and the stability of motion will be analyzed. Novel finite element formulations for open systems in coupled fluid and structural dynamics are presented.