A Generalized Tipping Condition for Arbitrary Geometric Objects Based on Contact Area and Applied Energy Using Cross Products

This work introduces a new energy-based model based on cross product torque analysis for the generalization of the tipping condition of rigid bodies of general shape. Classical mechanics employs torque to find rotational balance, but my method introduces the percent contact area (PCA) to define the extent to which the object is supported on a surface and how this influences tipping. The article presents a formula for computing the minimum amount of external energy to cause tipping by considering torque through the cross product and accounting for geometric distribution and weight. The PyBullet simulations yield high correlation, affirming the model's ability to make predictions