# Accession Number:

## ADA244194

# Title:

## Dynamical Systems Analysis of an Aerodynamic Decelerator's Behavior During the Initial Opening Process

# Descriptive Note:

## Final rept. Oct 1987-Sep 1991

# Corporate Author:

## ARMY NATICK RESEARCH DEVELOPMENT AND ENGINEERING CENTER MA

# Personal Author(s):

# Report Date:

## 1991-12-01

# Pagination or Media Count:

## 37.0

# Abstract:

A new mathematical model is developed and analyzed to determine the qualitative behavior of an aerodynamic decelerator during the initial opening phase. Currently, all models of canopy opening are valid only once the canopy has begun to inflate and has some assumed shape. The ability to determine the appropriate initial shape would greatly enhance these models. A set of elastodynamic equations for a simplified canopy model is nonlinearly coupler to Lighthills model for the relative velocity between a cylinder and the flow past it Previous work used a linear model for the fluid structure interaction. The new model presented in this paper removes this restriction by using a nonlinear interaction model. The resultant set of nonlinear partial differential equations is expended in terms of a complete set of eigenfunctions. The results is an infinite set of coupled ordinary differential equations in time. This set is then truncated to obtain various sets of low-dimensional models. These models are investigated to determine the stability of the canopy with respect to the fluids velocity, the line tension and the drag coefficients. Using dynamical system theory, an understanding of the bifurcation process is obtained without having to solve the full system of nonlinear partial differential equations. Hence, it is possible to predict the onset of divergence and flutter as a function of the system parameters in an efficient manner.

# Descriptors:

- *AERODYNAMICS
- *DECELERATION
- *OPENING(PROCESS)
- AERODYNAMIC CHARACTERISTICS
- CANOPIES
- COEFFICIENTS
- DIFFERENTIAL EQUATIONS
- DRAG
- DYNAMICS
- EIGENVECTORS
- ELASTIC PROPERTIES
- EQUATIONS
- FLUIDS
- FLUTTER
- INFINITE SERIES
- INTERACTIONS
- LINEAR SYSTEMS
- MATHEMATICAL MODELS
- MODELS
- NONLINEAR DIFFERENTIAL EQUATIONS
- NONLINEAR SYSTEMS
- PARAMETERS
- PARTIAL DIFFERENTIAL EQUATIONS
- SET THEORY
- SIMPLIFICATION
- STABILITY
- SYSTEMS ANALYSIS
- TENSION
- THEORY
- VELOCITY

# Subject Categories:

- Aerodynamics
- Manufacturing and Industrial Engineering and Control of Production Systems
- Mechanics