As trivial examples of Jacobi fields one can consider \dot\gamma(t) and t\dot\gamma(t).
Any Jacobi field J can be represented in a unique way as a sum T+I, where T=a\dot\gamma(t)+bt\dot\gamma(t) is a linear combination of trivial Jacobi fields and I(t) is orthogonal to \dot\gamma(t), for all t.