Date of download: 10/21/2017 Copyright © ASME. All rights reserved. From: Global Dynamics of an Autoparametric System With Multiple Pendulums J. Comput. Nonlinear Dynam. 2005;1(1):35-46. doi:10.1115/1.1994879 Figure Legend: A linear single degree-of-freedom (SDOF) system with n attached uncoupled pendulums

Date of download: 10/21/2017 Copyright © ASME. All rights reserved. From: Global Dynamics of an Autoparametric System With Multiple Pendulums J. Comput. Nonlinear Dynam. 2005;1(1):35-46. doi:10.1115/1.1994879 Figure Legend: Equilibrium solutions (P1,Q1,P2,Q2) for a two-pendulum system as a function of internal mistuning (d1) of pendulum 1. Different symbols represent different types of equilibrium solutions. System parameters: d2=0; ν1=ν2=1∕2; P00=1.

Date of download: 10/21/2017 Copyright © ASME. All rights reserved. From: Global Dynamics of an Autoparametric System With Multiple Pendulums J. Comput. Nonlinear Dynam. 2005;1(1):35-46. doi:10.1115/1.1994879 Figure Legend: Eigenvalues of equilibrium solutions for a two-pendulum system having both pendulums in motion at different values of pendulum 1 internal mistuning (d1). Big (small) symbols represent real (imaginary) parts of the eigenvalues. d2=0; ν1=ν2=1∕2; P00=1.

Date of download: 10/21/2017 Copyright © ASME. All rights reserved. From: Global Dynamics of an Autoparametric System With Multiple Pendulums J. Comput. Nonlinear Dynam. 2005;1(1):35-46. doi:10.1115/1.1994879 Figure Legend: Equilibrium solutions (P1,Q1,P2,Q2) as a function of internal mistuning (d1) of pendulum 1 for a two-pendulum system. Different symbols represent different types of equilibrium solutions. d2=0; ν1=1∕6, ν2=5∕6; P00=1.

Date of download: 10/21/2017 Copyright © ASME. All rights reserved. From: Global Dynamics of an Autoparametric System With Multiple Pendulums J. Comput. Nonlinear Dynam. 2005;1(1):35-46. doi:10.1115/1.1994879 Figure Legend: Eigenvalues of equilibrium solutions for a two-pendulum system having both pendulums in motion at different values of pendulum 1 internal mistuning (d1). Big (small) symbols represent real (imaginary) parts of the eigenvalues. d2=0; ν1=1∕6, ν2=5∕6; P00=1.

Date of download: 10/21/2017 Copyright © ASME. All rights reserved. From: Global Dynamics of an Autoparametric System With Multiple Pendulums J. Comput. Nonlinear Dynam. 2005;1(1):35-46. doi:10.1115/1.1994879 Figure Legend: Equilibrium solutions (P1,Q1,P2,Q2) as a function of internal mistuning (d1) of pendulum 1 for a two-pendulum system. Different symbols represent different types of equilibrium solutions. d2=0; ν1=5∕6, ν2=1∕6; P00=1.

Date of download: 10/21/2017 Copyright © ASME. All rights reserved. From: Global Dynamics of an Autoparametric System With Multiple Pendulums J. Comput. Nonlinear Dynam. 2005;1(1):35-46. doi:10.1115/1.1994879 Figure Legend: Eigenvalues of equilibrium solutions for a two-pendulum system having both pendulums in motion at different values of pendulum 1 internal mistuning (d1). Big (small) symbols represent real (imaginary) parts of the eigenvalues. d2=0; ν1=5∕6, ν2=1∕6; P00=1.

Date of download: 10/21/2017 Copyright © ASME. All rights reserved. From: Global Dynamics of an Autoparametric System With Multiple Pendulums J. Comput. Nonlinear Dynam. 2005;1(1):35-46. doi:10.1115/1.1994879 Figure Legend: Projection of Poincaré sections at cos2Q2=−0.15 on (P1,Q1) plane for motions started with three different initial conditions for an unperturbed two-pendulum system: (+ and ×) denote motions initiated near two center-saddles {(0.73,1.57,0,1.11) and (0.59,0,0,0.62)} with initial conditions (0.74,1.67,0.05,1.2) and (0.69,0.1,0.05,0.72), and (o) denotes motion initiated near a center-center (0.68,0,0.31,1.57) with initial conditions (0.78,0.1,0.21,1.67). d1=0.2, d2=0;ν1=5∕6, ν2=1∕6; δ=0, P00=1.

Date of download: 10/21/2017 Copyright © ASME. All rights reserved. From: Global Dynamics of an Autoparametric System With Multiple Pendulums J. Comput. Nonlinear Dynam. 2005;1(1):35-46. doi:10.1115/1.1994879 Figure Legend: Projection of Poincaré sections at cos2Q2=−0.15 on (P1,Q1) plane for motions started with three different initial conditions for a perturbed two-pendulum system with δ=0.02 and forcing F̂=2: (+ and ×) denote motions initiated near two center-saddles {(0.73,1.57,0,1.11) and (0.59,0,0,0.62)} with initial conditions (0.74,1.67,0.05,1.2) and (0.69,0.1,0.05,0.72), and (o) denotes motion initiated near a center-center (0.68,0,0.31,1.57) with initial conditions (0.78,0.1,0.21,1.67). d1=0.2, d2=0; ν1=5∕6, ν2=1∕6; P00=1.