TY - JOUR

T1 - Deterministic physical systems under uncertain initial conditions

T2 - The case of maximum entropy applied to projectile motion

AU - Montecinos, Alejandra

AU - Davis, Sergio

AU - Peralta, Joaquín

PY - 2018/5/17

Y1 - 2018/5/17

N2 - The kinematics and dynamics of deterministic physical systems have been a foundation of our understanding of the world since Galileo and Newton. For real systems, however, uncertainty is largely present via external forces such as friction or lack of precise knowledge about the initial conditions of the system. In this work we focus on the latter case and describe the use of inference methodologies in solving the statistical properties of classical systems subject to uncertain initial conditions. In particular we describe the application of the formalism of maximum entropy (MaxEnt) inference to the problem of projectile motion, given information about the average horizontal range over many realizations. By using MaxEnt we can invert the problem and use the provided information on the average range to reduce the original uncertainty in the initial conditions. Also, additional insight into the initial condition's probabilities, and the projectile path distribution itself, can be achieved based on the value of the average horizontal range. The wide applicability of this procedure, as well as its ease of use, reveals a useful tool with which to revisit a large number of physics problems, from classrooms to frontier research.

AB - The kinematics and dynamics of deterministic physical systems have been a foundation of our understanding of the world since Galileo and Newton. For real systems, however, uncertainty is largely present via external forces such as friction or lack of precise knowledge about the initial conditions of the system. In this work we focus on the latter case and describe the use of inference methodologies in solving the statistical properties of classical systems subject to uncertain initial conditions. In particular we describe the application of the formalism of maximum entropy (MaxEnt) inference to the problem of projectile motion, given information about the average horizontal range over many realizations. By using MaxEnt we can invert the problem and use the provided information on the average range to reduce the original uncertainty in the initial conditions. Also, additional insight into the initial condition's probabilities, and the projectile path distribution itself, can be achieved based on the value of the average horizontal range. The wide applicability of this procedure, as well as its ease of use, reveals a useful tool with which to revisit a large number of physics problems, from classrooms to frontier research.

KW - projectile motion

KW - maximum entropy

KW - inverse problem

UR - http://www.scopus.com/inward/record.url?scp=85049941034&partnerID=8YFLogxK

U2 - 10.1088/1361-6404/aaaf0c

DO - 10.1088/1361-6404/aaaf0c

M3 - Article

VL - 39

JO - European Journal of Physics

JF - European Journal of Physics

SN - 0143-0807

IS - 4

M1 - 045102

ER -