Absolutely, let's go through the process of updating the physical parameters to match the trajectories provided in 'problem_trajectories.txt'.

Given the constraints:
* The mass of the objects must not be changed.
* Physical parameters should not be modified beyond the first significant digit.

Here's a refined `example_code_1.py` to produce the required trajectories:

```python
# example_code_1.py

# Assuming the SIMULATOR_MODEL class and other necessary imports/methods are already defined
sim = SIMULATOR_MODEL()
sim.create_pusher('3.0 3.0 0.05')

# Physics parameters for the tray
physical_parameters_for_object_id_tray = { 
    'sliding-friction': 0.1,
    'armature': 0.1,
    'stiffness': 0.0,
    'mass': 0.5,
    'damping': 20
}

# Keeping the tray parameters as they don't need tweaks according to the problem statement
sim.create_tray(object_physics = physical_parameters_for_object_id_tray)


# Physics parameters for the bottle (20.0 mass)
physical_parameters_for_object_id_1 = { 
    'sliding-friction': 0.2,  # Updating based on expected motion
    'armature': 0.3,          # Initially 0.2
    'stiffness': 0.3,         # No change needed
    'mass': 20.0,             # Keeping mass constant
    'damping': 6.0,           # Initially 5.7
}

sim.create_object(object_id=1, object_name='bottle', object_location=('row_1', 'column_3'), object_color='orange', object_physics=physical_parameters_for_object_id_1)


# Physics parameters for the martini glass (10.0 mass)
physical_parameters_for_object_id_2 = { 
    'sliding-friction': 0.6,  # Initially 0.5
    'armature': 0.4,          # No change needed
    'stiffness': 1.0,         # No change needed
    'mass': 10.0,             # Keeping mass constant
    'damping': 8.0,           # Initially 8.8
}

sim.create_object(object_id=2, object_name='martini_glass', object_location=('row_1', 'column_2'), object_color='orange', object_physics=physical_parameters_for_object_id_2)


# Physics parameters for the wine glass (4.0 mass)
physical_parameters_for_object_id_3 = { 
    'sliding-friction': 0.6,  # No change needed
    'armature': 0.7,          # Initially 0.8
    'stiffness': 0.5,         # Initially 0.6
    'mass': 4.0,              # Keeping mass constant
    'damping': 7.0,           # Initially 8.3
}

sim.create_object(object_id=3, object_name='wine_glass', object_location=('row_1', 'column_1'), object_color='orange', object_physics=physical_parameters_for_object_id_3)


# Create and simulate the scene
sim.create_scene()
sim_out=sim.run_simulation()

# Clean up
del sim
```

Key Updates and Assumptions:
1. **Bottle:** Increased damping slightly (5.7 to 6.0) and sliding friction (0.1 to 0.2). Armature adjusted from 0.2 to 0.3 based on trajectory changes.
2. **Martini Glass:** Increased sliding friction slightly (0.5 to 0.6), slightly reduced damping (8.8 to 8.0), and retained the original armature and stiffness.
3. **Wine Glass:** Reduced armature from 0.8 to 0.7, reduced stiffness from 0.6 to 0.5, and damping significantly from 8.3 to 7.0, keeping sliding friction constant.

By making these adjustments, we aim to replicate the required trajectories for each object as closely as possible. Re-run the simulation with these parameters to check if it matches the `problem_trajectories.txt`.