FORZE

• $F\_p\; =\; -mg\backslash hat\{k\}$ FORZA PESO
• $F\_e\; =\; -k(\backslash Delta\; -\; e)\backslash hat\{u\}$ FORZA ELASTICA
• con $\backslash Delta\; =\; |P-O|$ lunghezza molla
• e = l. nulla a riposo
• Se l=o
• $F\_e\; =\; -k(P-O)$
• $F\_v\; =\; \backslash gamma\backslash dot\{v\}$ FORZA VISCOSA

• GRADIENTE $\backslash nabla\; f(x,y,z)\; =\; \backslash dfrac\{\backslash partial\; f\}\{\backslash partial\; x\}\backslash hat\{i\}\; +\; \backslash dfrac\{\backslash partial\; f\}\{\backslash partial\; y\}\backslash hat\{j\}\; +\; \backslash dfrac\{\backslash partial\; f\}\{\backslash partial\; z\}\backslash hat\{k\}$
• ROTORE $rot\; \backslash vec\{F\}(x,y,z)\; =\; \backslash nabla\; \backslash times\; \backslash vec\{F\}$

• 	$\backslash hat\{i\}$	$\backslash hat\{j\}$	$\backslash hat\{k\}$
  	$\backslash dfrac\{\backslash partial\}\{\backslash partial\; x\}$	$\backslash dfrac\{\backslash partial\}\{\backslash partial\; y\}$	$\backslash dfrac\{\backslash partial\}\{\backslash partial\; z\}$
  	$F\_x$	$F\_y$	$F\_z$

• $\backslash vec\{F\}$ campo di forze conservativo $\backslash Rightarrow\; rot\; \backslash vec\{F\}(x,y,z)\; =\; \backslash vec\{0\}$ (se dominio di $\backslash vec\{F\}$ è semplic. connesso)

• un campo vettoriale è CONSERVATIVO se una funz. scalare $V(x,y,z)t$ t.c. $\backslash vec\{F\}(x,y,z)\; =\; -\backslash nabla\; V(x,\; y,\; z)$ ENERGIA POTENZIALE

• Moto punto materiale vincolato $m\backslash vec\{a\}=\; \backslash vec\{F\}\; +\; \backslash vec\{F\}$ EQUAZIONE DEL MOTO