What Are the Higher Moments of Force and Their Role in Particle Motion?

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Higher moments of force, beyond the first moment (torque), raise questions about their relevance in particle motion. While Newton's laws effectively describe translation and rotation through force and torque, the implications of second and higher moments are less clear. These higher moments could theoretically compress or stretch objects, but their significance diminishes when considering rigid bodies. The discussion suggests that for rigid objects, higher moments may lack practical physical meaning. Further literature on this topic is requested for deeper understanding.
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Thinking about Newton's laws, one can see that they concern the force and the torque (the first moment of the force) acting on a particle. That is enough to describe translation and rotation. But, is there something more to this? What about second and higher moment of the force? Is there any obvious reason they don't have any physical meaning?
 
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They would compress/stretch the object. If you assume rigid objects, they are irrelevant.
 
Well that sounds plausible. Thanks for the answer. Can you refer me to the relevant literature?
 

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