There is a well-known $N$-body problem in classical mechanics: Given an initial positions and velocities of $N$ particles in some space, describe their dynamics over some time interval.

I'm interested in some from of "inverse" problem: Let's assume that we know that there are $(N+1)$ particles in some space. We are given the trajectories of $N$ of these particles over some time interval. The problem is to restore the trajectory of the $(N+1)$-th particle over the same time interval.

The underlying force field is assumed to be known. For example, we can assume that each pair of particles is attracted according to the inverse square law.

What is a correct generally accepted name for this problem? Is this problem described in literature?

There is a well-known $N$-body problem in classical mechanics: Given an initial positions and velocities of $N$ particles in some space, describe their dynamics over some time interval.

I'm interested in some form of "inverse" problem: Let's assume that we know that there are $(N+1)$ particles in some space. We are given the trajectories of $N$ of these particles over some time interval. The problem is to restore the trajectory of the $(N+1)$-th particle over the same time interval.

The underlying force field is assumed to be known. For example, we can assume that each pair of particles is attracted according to the inverse square law.

What is a correct generally accepted name for this problem? Is this problem described in literature?

There is a well-known N-body problem in classical mechanics: Given an initial positions and velocities of N particles in some space, describe their dynamics over some time interval.

I'm interested in some from of "inverse" problem: Let's assume that we know that there are (N+1) particles in some space. We are given the trajectories of N of these particles over some time interval. The problem is to restore the trajectory of the (N+1)-th particle over the same time interval.

The underlying force field is assumed to be known. For example, we can assume that each pair of particles is attracted according to the inverse square law.

What is a correct generally accepted name for this problem? Is this problem described in literature?

There is a well-known $N$-body problem in classical mechanics: Given an initial positions and velocities of $N$ particles in some space, describe their dynamics over some time interval.

I'm interested in some from of "inverse" problem: Let's assume that we know that there are $(N+1)$ particles in some space. We are given the trajectories of $N$ of these particles over some time interval. The problem is to restore the trajectory of the $(N+1)$-th particle over the same time interval.

The underlying force field is assumed to be known. For example, we can assume that each pair of particles is attracted according to the inverse square law.

What is a correct generally accepted name for this problem? Is this problem described in literature?