\left\{\text{x1}'(t) \sin (\text{x2}(t))=\text{x4}(t) \sin (\text{x3}(t))+\text{x5}(t) \cos (\text{x3}(t)),\text{x2}'(t)=\text{x4}(t) \cos (\text{x3}(t))-\text{x5}(t) \sin (\text{x3}(t)),\text{x1}'(t) \cos (\text{x2}(t))+\text{x3}'(t)=a,\text{x4}'(t)-a (1-\lambda ) \text{x5}(t)=-m \sin (\text{x2}(t)) \cos (\text{x3}(t)),a (1-\lambda ) \text{x4}(t)+\text{x5}'(t)=m \sin (\text{x2}(t)) \sin (\text{x3}(t))\right\}