Depending on what you define “sudden change” as, neural networks might be unnecessary, and you might be able to find the points using the angle of change.
If not, you can try sequence to sequence networks. One way to do so would be following,
1. For each point on the trajectory, calculate the angle between previous and next trajectory. That is for x(i), calculate angle formed by x(i – 1) and x(i + 1). For robustness, you could consider more points.
2. For output, use sequence of 0s and 1s, where 1 is when the object made sudden change, and 0 otherwise.