Studiamo il caso di una traiettoria su un arco di circonferenza di centro C e raggio R con inizio nel punto A sull'asse y ([math]A>0[/math]) e fine nel punto B sull'asse x ([math]B\geq0[/math]). [br][br]Consideriamo un corpo di massa m che si muove lungo questa traiettoria sottoposto alla sola azione della forza peso. 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[/img][br][br]Supponiamo, senza perdita di generalità, che il punto B della circonferenza abbia come tangente l'asse x. Supponiamo inoltre che tutta la massa del sistema sia concentrata nel corpo di massa m.[br]In tal modo il problema si riconduce alla "teoria del pendolo semplice".[br][br]Ovviamente il corpo, a causa della traiettoria, si può solo muovere lungo l'arco di circonferenza e si ha a che fare con un moto circolare con accelerazione variabie. [br]Il corpo e' soggetto a due accelerazioni, una tangenziale alla circonferenza ed una centripeta diretta verso il suo centro.[br][br]Detta [math]a_t[/math] la componente tangenziale dell'accelerazione e [math]\theta\left(t\right)[/math] l'angolo che individua la posizione di m al tempo t, risulta:[br][br][math]a_t=-g\cdot sen\theta\left(t\right)[/math].[br][br]Si ha poi, detto s l'arco di traiettoria individuato dall'angolo [math]\theta\left(t\right)[/math],[br][br][math]s=\theta\cdot R[/math] [br][br]dalla quale si ottiene, derivando[br][br][math]a_t=s''=\theta''\cdot R[/math].[br][br]Euguagliando le due espressioni di [math]a_t[/math] si ottiene:[br][br][math]\theta''\cdot R=-g\cdot sen\theta\left(t\right)[/math][br][br]cioè[br][br][math]\theta''+\frac{g}{R}\cdot sen\theta\left(t\right)=0[/math].[br][br]Non è possibile trovare una soluzione semplice di questa equazione differenziale nei termini di una funzione elementare (la sua risoluzione porterebbe ad un integrale ellittico di prima specie risolvibile eventualmente con sviluppo in serie).[br]Considerando piccoli valori dell'angolo [math]\theta[/math] possiamo approssimare [br][math]sen\theta\left(t\right)[/math] con [math]\theta\left(t\right)[/math].[br][br]In tal modo l'equazione differenziale si semplifica in[br][br][math]\theta''+\frac{g}{R}\cdot \theta\left(t\right)=0[/math][br][br]che è facilmente risolvibile ed ha soluzione:[br][br][math]\theta\left(t\right)=\theta_0\cdot cos\left(\sqrt\frac{g}{R} t\right)[/math].[br][br][br]Ricaviamo ora le equazioni del moto considerando la generica equazione di una circonferenza di Centro [math]C(x_{0},y_{0})[/math] e raggio R:[br][br][math]\left(x-x_{c}\right)^{2}+\left(y-y_{c}\right)^{2}=R^{2}[br] [/math], [br][br]esprimibile anche in forma parametrica (usando il parametro angolare [math]\theta\left(t\right)[br] [/math] calcolato a partire da CB in direzione antioraria):[br][br][math][br]\begin{cases}[br]\begin{array}{l}[br]x=x_{c}+R\cdot sen\left(\theta\left(t\right)\right)\\[br]y=y_{c}+R\cdot cos\left(\theta\left(t\right)\right)[br]\end{array}\end{cases}[br][/math][br][br]Detti [math]\theta_{0}[br] [/math] (angolo negativo) e [math]\theta_{f}=0[br] [/math] rispettivamente gli angoli che individuano i punti [math]\left(0,A\right)[br] [/math] e [math]\left(B,0\right)[br] [/math] si ha[br][br][math]\theta_f=\theta\left(t_f\right)=\theta_0\cdot cos\left(\sqrt\frac{g}{R} t_f\right)[/math][br][br]dalla quale[br][br][math]t_f=\sqrt\frac{R}{g} \cdot arccos\left(\frac{\theta_f}{\theta_0}\right)[/math].[br][br]E' possibile infine calcolare la velocità ed accelerazione tangenziale di m:[br][br][math]v_t=s'=\theta'\cdot R=-\theta_0\sqrt{gR} \cdot sen \left(\sqrt\frac{g}{R} t\right)[/math][br][br][math]a_t=s''=\theta''\cdot R=-g \cdot \theta\left(t\right)[/math].[br]