I have repeatedly noticed that some (too many) people have difficulties understanding or even applying the concept of a Schwerpunkt.
Me personally, I don't get it at all.
What's so difficult about it? I don't get it.
Clausewitz applied this (his) concept a couple times in his writings, with some deviations. I'll do a summary of the general idea and its later shapes:
Superior* armies tend to prevail over inferior ones.
Thus you better make sure to have the superior army before accepting, offering or forcing battle.
The enemy isn't dumb and attempts the same, so you need a resolute concentration of force to best him in this.
We live in a world of scarcity; neither you nor your opponent have infinite forces at disposal.
This means in order to amass a superior army, you need to strictly limit your strength elsewhere.**
This is contrary to man's risk aversion, and thus it's the real challenge in the whole concept.***
The original Clausewitzian Schwerpunkt is unrelated to Newtonian physics. Clausewitz got Newtonian physics clearly wrong and borrowed a word whose mechanical meaning he did not understand. Simply ignore the physics in regard to the military Schwerpunkt.
Clausewitz' Schwerpunkt was about the strategic level and the decisive battle; theatre command / campaign or war strategy as a whole. He also used it in the context of the main battle. It was a design for a Napoleon-ish leader.
Later German military use of the concept expanded the basic idea to all levels, down to people calling the machinegun the Schwerpunktwaffe (Schwerpunkt weapon) of the German WW2 infantry squad leader.
So basically if you want to do something, do it right - and be prepared to accept that some other things won't turn out so well since you need to neglect them.
Post-Second World War (at the latest), Schwerpunkt entered civilian German in a meaning akin to the military one. Nowadays you can say it instead of Fokus and some other words.
The Americans kind of didn't like Clausewitz' Schwerpunkt. Maybe they didn't care much about resource constraints, maybe the horrible translations (inaccurate, but much more readable than the original) are to blame.
They basically went all in on the idea that if you defeat the Schwerpunkt of the enemy, you ought to have won (which Clausewitz kind of wrote). This was warped into the American idea of a military 'center of gravity': It describes a critical vulnerability of the enemy. It is a kind of supposedly existing trigger which allows you to defeat the enemy with little effort. Divisional headquarters, heads of state, national electrical grid hubs and the like become a 'center of gravity' in this view.
Clausewitz rolls over in his grave, for the enemy's Schwerpunkt was in his concept the most difficult to defeat thing there is.
I hope at least the few hundred readers of this blog won't have any problems with Schwerpunkt in its military meaning in the future. My advice is to write "center of gravity"(not British English: "centre ...") if you mean the American idea of a critical vulnerability / I-win-button and "Schwerpunkt" if you mean the German interpretation.
Don't bother with the needlessly restrictive Clausewitzian version (for high command only) unless there's an academic debate specifically about Clausewitz' post-mortem book "Vom Kriege" ("On war").
2010-01 Schwerpunkt and "center of gravity"
2010-08 Schwerpunkt and "Klotzen, nicht kleckern!" - the balance problem
"Vom Kriege", online for free
"On war", online for free (Graham translation)
*: Taking into account both quality and quantity.
**: "He who defends everything defends nothing." Frederick II the Great; pre-Clausewitz.
***: German language knows the phrase "scharf zusammenfassen", expressing that forces will not only be accumulated for the Schwerpunkt action the normal way, but by overcoming resistances and preferences.
Compare the U.S.Army terminology of "economy of force"..