Large Amplitude Oscillations of a Double Pendulum

POSTER

Abstract

The nature of the normal modes of oscillation in the small angle regime of a double pendulum is well established. However, for large amplitude oscillations, a closed form solution of the differential equations of motion does not exist. Using Lagrange formalism, we explore both the in-phase and out-of-phase normal modes of oscillation of a double pendulum as a function of the mass ratio of the two bobs and their initial angular positions. We conduct the analysis using MatLab, where we initially verify our code in the known small amplitude limit. Among our results we find that certain symmetries between the in-phase and out-of-phase normal modes that exist in the small amplitude limit are no longer present at large amplitudes.

Authors

  • Kyung Yu

    University of Akron, Youngstown State University, Shady Side Academy, Westminster College, Nitronex Corporation, Durham, NC, AFRL,Wright-Patterson AFB, Ohio, University of Michigan, Ann Arbor, Department of Physics, The Ohio State University, Lunghwa University of Science and Technology, Eastern Michigan University, Wright State University, Michigan State University, Texas A\&M University and Princeton University, Joint Institute for Nuclear Research (Dubna), Naval Research Laboratory, ManTech SRS Technologies, Inc., Ecopulse, Inc., Army Research Laboratory, University of Surrey, Kettering University, Flint, MI, Pennsylvania State University, University of TN

  • Kyung Yu

    University of Akron, Youngstown State University, Shady Side Academy, Westminster College, Nitronex Corporation, Durham, NC, AFRL,Wright-Patterson AFB, Ohio, University of Michigan, Ann Arbor, Department of Physics, The Ohio State University, Lunghwa University of Science and Technology, Eastern Michigan University, Wright State University, Michigan State University, Texas A\&M University and Princeton University, Joint Institute for Nuclear Research (Dubna), Naval Research Laboratory, ManTech SRS Technologies, Inc., Ecopulse, Inc., Army Research Laboratory, University of Surrey, Kettering University, Flint, MI, Pennsylvania State University, University of TN

  • Kyung Yu

    University of Akron, Youngstown State University, Shady Side Academy, Westminster College, Nitronex Corporation, Durham, NC, AFRL,Wright-Patterson AFB, Ohio, University of Michigan, Ann Arbor, Department of Physics, The Ohio State University, Lunghwa University of Science and Technology, Eastern Michigan University, Wright State University, Michigan State University, Texas A\&M University and Princeton University, Joint Institute for Nuclear Research (Dubna), Naval Research Laboratory, ManTech SRS Technologies, Inc., Ecopulse, Inc., Army Research Laboratory, University of Surrey, Kettering University, Flint, MI, Pennsylvania State University, University of TN

  • Kyung Yu

    University of Akron, Youngstown State University, Shady Side Academy, Westminster College, Nitronex Corporation, Durham, NC, AFRL,Wright-Patterson AFB, Ohio, University of Michigan, Ann Arbor, Department of Physics, The Ohio State University, Lunghwa University of Science and Technology, Eastern Michigan University, Wright State University, Michigan State University, Texas A\&M University and Princeton University, Joint Institute for Nuclear Research (Dubna), Naval Research Laboratory, ManTech SRS Technologies, Inc., Ecopulse, Inc., Army Research Laboratory, University of Surrey, Kettering University, Flint, MI, Pennsylvania State University, University of TN

  • Kyung Yu

    University of Akron, Youngstown State University, Shady Side Academy, Westminster College, Nitronex Corporation, Durham, NC, AFRL,Wright-Patterson AFB, Ohio, University of Michigan, Ann Arbor, Department of Physics, The Ohio State University, Lunghwa University of Science and Technology, Eastern Michigan University, Wright State University, Michigan State University, Texas A\&M University and Princeton University, Joint Institute for Nuclear Research (Dubna), Naval Research Laboratory, ManTech SRS Technologies, Inc., Ecopulse, Inc., Army Research Laboratory, University of Surrey, Kettering University, Flint, MI, Pennsylvania State University, University of TN

  • Kyung Yu

    University of Akron, Youngstown State University, Shady Side Academy, Westminster College, Nitronex Corporation, Durham, NC, AFRL,Wright-Patterson AFB, Ohio, University of Michigan, Ann Arbor, Department of Physics, The Ohio State University, Lunghwa University of Science and Technology, Eastern Michigan University, Wright State University, Michigan State University, Texas A\&M University and Princeton University, Joint Institute for Nuclear Research (Dubna), Naval Research Laboratory, ManTech SRS Technologies, Inc., Ecopulse, Inc., Army Research Laboratory, University of Surrey, Kettering University, Flint, MI, Pennsylvania State University, University of TN

  • Kyung Yu

    University of Akron, Youngstown State University, Shady Side Academy, Westminster College, Nitronex Corporation, Durham, NC, AFRL,Wright-Patterson AFB, Ohio, University of Michigan, Ann Arbor, Department of Physics, The Ohio State University, Lunghwa University of Science and Technology, Eastern Michigan University, Wright State University, Michigan State University, Texas A\&M University and Princeton University, Joint Institute for Nuclear Research (Dubna), Naval Research Laboratory, ManTech SRS Technologies, Inc., Ecopulse, Inc., Army Research Laboratory, University of Surrey, Kettering University, Flint, MI, Pennsylvania State University, University of TN

  • Marshall Thomsen

    Eastern Michigan University

  • Kyung Yu

    University of Akron, Youngstown State University, Shady Side Academy, Westminster College, Nitronex Corporation, Durham, NC, AFRL,Wright-Patterson AFB, Ohio, University of Michigan, Ann Arbor, Department of Physics, The Ohio State University, Lunghwa University of Science and Technology, Eastern Michigan University, Wright State University, Michigan State University, Texas A\&M University and Princeton University, Joint Institute for Nuclear Research (Dubna), Naval Research Laboratory, ManTech SRS Technologies, Inc., Ecopulse, Inc., Army Research Laboratory, University of Surrey, Kettering University, Flint, MI, Pennsylvania State University, University of TN