Generating codim-1 bifurcation diagram of sliding friction oscillator
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I am performing continuation analysis in MATCONT and I am finding it difficult to generate co-dim bifurcation diagram.
Here is my linearized system of equations which represents a 3-dof clutch dynamics with sliding type friction:
x1' = x2
x2' = -(de+Fn*mukin)*x2/je + (Fn*mukin*x4)/je - ((x2-x4)*mukin + mus)/je
x3' = x4
x4' = (Fn*mukin*x2)/jd - (ds+Fn*mukin)*x4/jd +ds*x6/jd + ks*x7/jd
x5' = x6
x6' = ds*x4/jv -ds*x6/jv - ks*x7/jv
x7' = x6 - x4
This system dynamics represents clutch dynamics with the sliding friction between inertias je and jd. jv is the load inertia. ks is stiffness between jd and jv. de,ds is damping coefficient. Fn is normal force acting on jd and je during engagement of clutch. mukin is slope of friction curve usually between [-0.01 to 0.01] and mus is static coefficient of friction 0.136 for this analysis.
je = 1.57
jd = 0.0066
jv = 4
ks = 56665.5
ds,de = 0.1
Fn = 8000
Please guide me how to perform the continuation of this system in MATCONT.
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