The principles of statics without force I'm a student of civil engineering and now my course is covering the basics of statics, such as the equations of equilibrium, etc. Trying to get a better basis on the subject, I started to search on the subject of force and plane statics. I found in https://archive.org/details/ConceptsOfForce the confirmation of what I had already read on Russell's Principles of Mathematics: that the concept of force is totally fictious, and modern science is in a growing tendency of abandon it. My question is: how the principles of statics (specially the equations of equilibrium) would be formulated without the aid of "force"? In Jammer's book, he explains the meaning of Newton's second law (i.e, mass times acceleration) as a function of configuration, but I fail to see how this would apply.
Have a nice day.
 A: Principles of statics is a consequence of the principle of minimum of potential energy.
You could write down the full potential energy of the system $U(x _1,\ ...,\ x_n)$ and minimize it regarding constraints equations $F_k(x _1,\ ...,\ x_n)=0.$ Doing it using Lagange multipliers you'll obtain equations of static: 
$$\frac {\partial U}{\partial x _i } - \sum\limits_k \lambda_k \frac {\partial F_k}{\partial x_i }=0,$$
$$F_k(x _1,\ ...,\ x_n)=0.$$
You also could find out how is it related to (generalized) forces keeping in mind that force acting to some part of the system is just a negative gradient of the potential energy by the coordinates of this part.
A: I'm not sure that the concept of a force is fictitious. I've heard Engineers say that forces aren't real and that there are only couples, but I wonder if this is more about semantics than anything else. It seems like physicists are always inventing new forces! To me, a force is something you put on the right hand side of the second derivative of some quantity with respect to some parameter (akin to the idea of generalized forces in analytical mechanics). Sure, I can almost always choose a parametrization such that the force vanishes, but if you call that fictitious then you'd have to say that dynamics are fictitious too! Personally I'm not going to disagree with that statement, but I don't think it is a position that modern science is gravitating towards.
