How to rigidly attach a Sphere to a CosseratRod?

[Qin-Shaowen]

I am simulating a rubber band with a metal ball tied to its end. The rubber band is modeled as a CosseratRod, and the ball is modeled as a Sphere. In reality, the ball is tightly tied to the rubber band, so the connection should be very stiff — the ball is essentially a rigid extension of the rod's end.

Currently, I connect the rod and sphere using a FixedJoint:

system.connect(rod, sphere, first_connect_idx=-1, second_connect_idx=0).using(
    FixedJoint,
    k=1e2,
    nu=0.0,
    kt=1e-3,
    nut=0.0,
    rest_rotation_matrix=get_relative_rotation_two_systems(rod, -1, sphere, 0),
)

This works, but the connection is physically too soft. When I try to increase the stiffness to physically realistic values based on the rod's material properties, the simulation produces NaN.

My questions:

1. Is there a way in PyElastica to directly attach a Sphere to the end of a CosseratRod without using a Flexible Joint? For example, adding the sphere's mass and inertia directly to the rod's end node?
2. If FixedJoint is the correct approach, how should I set the parameters to simulate a very stiff, physically realistic connection without causing numerical instability?

Thank you for your help.