A closed form solution to the single degree of freedom simultaneous localisation and map building (SLAM) problem

2002 ◽  
Author(s):  
P.W. Gibbens ◽  
G.M.W.M. Dissanayake ◽  
H.F. Durrant-Whyte
Keyword(s):  
Closed Form ◽  
Closed Form Solution ◽  
Form Solution ◽  
Degree Of Freedom ◽  
Map Building ◽  
Single Degree Of Freedom ◽  
Single Degree

On Free Vibrations With Combined Viscous and Coulomb Damping

1980 ◽  
Vol 102 (4) ◽  
pp. 283-286 ◽  
Author(s):  
P. H. Markho
Keyword(s):  
Decay Curve ◽  
Closed Form Solution ◽  
Free Vibrations ◽  
Form Solution ◽  
Forced Response ◽  
Experimental Plot ◽  
Damping Force ◽  
Single Degree Of Freedom ◽  
Coulomb Damping ◽  
Single Degree

A closed-form solution of the governing, nonlinear equation for free vibrations of a single-degree-of-freedom system, without stops, under combined viscous and Coulomb damping is first obtained. This is much less involved than forced-response considerations of the same system (with or without stops) the solution of which problem was first obtained by Den Hartog [1]. This note contains the first derivation, as far as the author is aware of, of the equation for the amplitude decay curve (or envelope) for such a system vibrating freely under no-stop conditions. This equation is presented in a form which enables the components of the damping force to be determined from the system’s experimental plot (or record) of displacement versus time.

Optimal Isolation of a Single-Degree-of-Freedom System With Quadratic-Velocity Damping

1981 ◽  
Vol 48 (3) ◽  
pp. 676-678 ◽  
Author(s):  
T. L. Alley
Keyword(s):  
Closed Form ◽  
Simple Formula ◽  
Degree Of Freedom ◽  
Isolation System ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Linear Spring ◽  
Velocity Input

The response of a mass isolated by a linear spring and a quadratic-velocity damper subjected to a step-and-decay velocity input at the base is found in closed form. This solution leads immediately to the optimal isolation system for this input. The parameters of the optimal isolation system are given by a simple formula.

A Polynomial Equation for a Coupler Curve of the Double Butterfly Linkage

2000 ◽  
Vol 124 (1) ◽  
pp. 39-46 ◽  
Author(s):  
Gordon R. Pennock ◽  
Atif Hasan
Keyword(s):  
Closed Form ◽  
Systematic Approach ◽  
Polynomial Equation ◽  
Degree Of Freedom ◽  
Special Point ◽  
Eighth Order ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Original Contribution ◽  
Curve Equation

This paper presents a closed-form polynomial equation for the path of a point fixed in the coupler links of the single degree-of-freedom eight-bar linkage commonly referred to as the double butterfly linkage. The revolute joint that connects the two coupler links of this planar linkage is a special point on the two links and is chosen to be the coupler point. A systematic approach is presented to obtain the coupler curve equation, which expresses the Cartesian coordinates of the coupler point as a function of the link dimensions only; i.e., the equation is independent of the angular joint displacements of the linkage. From this systematic approach, the polynomial equation describing the coupler curve is shown to be, at most, forty-eighth order. This equation is believed to be an original contribution to the literature on coupler curves of a planar eight-bar linkage. The authors hope that this work will result in the eight-bar linkage playing a more prominent role in modern machinery.

Parametric Identification of a Vibratory System With a Clearance

1993 ◽  
Vol 115 (1) ◽  
pp. 25-32 ◽  
Author(s):  
R. M. Alexander ◽  
S. T. Noah ◽  
C. G. Franck
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Closed Form ◽  
Piecewise Linear ◽  
Closed Form Solution ◽  
Element Model ◽  
Form Solution ◽  
Degree Of Freedom ◽  
Vibratory System ◽  
Experimental Structure

An analytical and experimental investigation of a vibratory system with a clearance was conducted. A finite element model and an equivalent single-degree-of-freedom closed-form solution were used to determine the dynamic parameters and response of an experimental structure interacting with a gap. The closed-form solution is obtained by taking advantage of the piecewise linearity of the system. Results from these solution methods are in agreement with experimental data. The results also suggest that the closed-form solution approximates the response of the experimental structure with accuracy greater than that of the finite element model. The closed-form solution was also used to determine the gap size of the structure. The parameter identification procedure utilized in this study appears to be simple to use and can be readily extended to other types of piecewise-linear multi-degree-of-freedom systems.

On a Closed-Form Solution of Prandtl's System of Equations

2013 ◽  
Vol 40 (2) ◽  
pp. 106-114
Author(s):  
J. Venetis ◽  
Aimilios (Preferred name Emilios) Sideridis
Keyword(s):  
Closed Form ◽  
Closed Form Solution ◽  
Form Solution ◽  
System Of Equations
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