George Berkeley
Berkeley argued that forces and gravity, as defined by Newton, constituted "occult qualities" that "expressed nothing distinctly". He held that those who posited "something unknown in a body of which they have no idea and which they call the principle of motion, are in fact simply stating that the principle of motion is unknown." Therefore, those who "affirm that active force, action, and the principle of motion are really in bodies are adopting an opinion not based on experience." Forces and gravity existed nowhere in the phenomenal world. On the other hand, if they resided in the category of "soul" or "incorporeal thing", they "do not properly belong to physics" as a matter. Berkeley thus concluded that forces lay beyond any kind of empirical observation and could not be a part of proper science. He proposed his theory of signs as a means to explain motion and matter without reference to the "occult qualities" of force and gravity.
Castigliano's method
Castigliano's method, named for Carlo Alberto Castigliano, is a method for determining the displacements of a linear-elastic system based on the partial derivatives of the energy. He is known for his two theorems. The basic concept may be easy to understand by recalling that a change in energy is equal to the causing force times the resulting displacement. Therefore, the causing force is equal to the change in energy divided by the resulting displacement. Alternatively, the resulting displacement is equal to the change in energy divided by the causing force. Partial derivatives are needed to relate causing forces and resulting displacements to the change in energy. 
Castigliano's method for calculating forces is an application of his first theorem, which states:
In equation form,
where U is the strain energy.