Role of initial conditions in the dynamics of a double pendulum at low energies View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

2013-03-29

AUTHORS

Jyotirmoy Roy, Asok K. Mallik, Jayanta K. Bhattacharjee

ABSTRACT

We consider the low energy dynamics of the double pendulum. Low energy implies energies close to the critical value required to make the outer pendulum rotate. All the known interesting results for the double pendulum are at high energies, that is, energies higher than that required to make both pendulums rotate. We show that interesting behavior can occur at low energies as well by which we mean energies just sufficient to make the outer pendulum rotate. A harmonic balance and the Lindstedt–Poincare analysis at the low energies establish that at small, but finite amplitude; the two normal modes behave differently. While the frequency of the “in-phase” mode is almost unchanged with increasing amplitude, the frequency of the “out-of-phase” mode drops sharply. Numerical analysis verifies this analytic result and since the perturbation theory indicates a mode softening for the out-of-phase mode at a critical amplitude, we did a careful numerical analysis of the low energy region just above the threshold for onset of rotation for the outlying pendulum. We find chaotic behavior, but the chaos is a strong function of the initial condition. More... »

PAGES

993-1004

References to SciGraph publications

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s11071-013-0848-1

DOI

http://dx.doi.org/10.1007/s11071-013-0848-1

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1029407189


Indexing Status Check whether this publication has been indexed by Scopus and Web Of Science using the SN Indexing Status Tool
Incoming Citations Browse incoming citations for this publication using opencitations.net

JSON-LD is the canonical representation for SciGraph data.

TIP: You can open this SciGraph record using an external JSON-LD service: JSON-LD Playground Google SDTT

[
  {
    "@context": "https://springernature.github.io/scigraph/jsonld/sgcontext.json", 
    "about": [
      {
        "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/01", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Mathematical Sciences", 
        "type": "DefinedTerm"
      }, 
      {
        "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/0101", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Pure Mathematics", 
        "type": "DefinedTerm"
      }
    ], 
    "author": [
      {
        "affiliation": {
          "alternateName": "UM-DAE Centre for Excellence in Basic Sciences, Santa Cruz(E), 400098, Mumbai, India", 
          "id": "http://www.grid.ac/institutes/grid.452882.1", 
          "name": [
            "UM-DAE Centre for Excellence in Basic Sciences, Santa Cruz(E), 400098, Mumbai, India"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Roy", 
        "givenName": "Jyotirmoy", 
        "id": "sg:person.016070707602.84", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.016070707602.84"
        ], 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "alternateName": "S. N. Bose National Centre for Basic Science, Salt Lake, 700098, Kolkata, India", 
          "id": "http://www.grid.ac/institutes/grid.452759.8", 
          "name": [
            "S. N. Bose National Centre for Basic Science, Salt Lake, 700098, Kolkata, India"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Mallik", 
        "givenName": "Asok K.", 
        "id": "sg:person.016276051627.98", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.016276051627.98"
        ], 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "alternateName": "Harish-Chandra Research Institute, Jhunsi, 211019, Allahabad, India", 
          "id": "http://www.grid.ac/institutes/grid.450311.2", 
          "name": [
            "Harish-Chandra Research Institute, Jhunsi, 211019, Allahabad, India"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Bhattacharjee", 
        "givenName": "Jayanta K.", 
        "id": "sg:person.015365735162.55", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.015365735162.55"
        ], 
        "type": "Person"
      }
    ], 
    "citation": [
      {
        "id": "sg:pub.10.1007/s12043-009-0099-3", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1021542691", 
          "https://doi.org/10.1007/s12043-009-0099-3"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/s11071-007-9270-x", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1049100526", 
          "https://doi.org/10.1007/s11071-007-9270-x"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/s11071-012-0378-2", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1049168943", 
          "https://doi.org/10.1007/s11071-012-0378-2"
        ], 
        "type": "CreativeWork"
      }
    ], 
    "datePublished": "2013-03-29", 
    "datePublishedReg": "2013-03-29", 
    "description": "We consider the low energy dynamics of the double pendulum. Low energy implies energies close to the critical value required to make the outer pendulum rotate. All the known interesting results for the double pendulum are at high energies, that is, energies higher than that required to make both pendulums rotate. We show that interesting behavior can occur at low energies as well by which we mean energies just sufficient to make the outer pendulum rotate. A\u00a0harmonic balance and the Lindstedt\u2013Poincare analysis at the low energies establish that at small, but finite amplitude; the two normal modes behave differently. While the frequency of the \u201cin-phase\u201d mode is almost unchanged with increasing amplitude, the frequency of the \u201cout-of-phase\u201d mode drops sharply. Numerical analysis verifies this analytic result and since the perturbation theory indicates a mode softening for the out-of-phase mode at a critical amplitude, we did a careful numerical analysis of the low energy region just above the threshold for onset of rotation for the outlying pendulum. We find chaotic behavior, but the chaos is a strong function of the initial condition.", 
    "genre": "article", 
    "id": "sg:pub.10.1007/s11071-013-0848-1", 
    "inLanguage": "en", 
    "isAccessibleForFree": false, 
    "isPartOf": [
      {
        "id": "sg:journal.1040905", 
        "issn": [
          "0924-090X", 
          "1573-269X"
        ], 
        "name": "Nonlinear Dynamics", 
        "publisher": "Springer Nature", 
        "type": "Periodical"
      }, 
      {
        "issueNumber": "1-2", 
        "type": "PublicationIssue"
      }, 
      {
        "type": "PublicationVolume", 
        "volumeNumber": "73"
      }
    ], 
    "keywords": [
      "double pendulum", 
      "numerical analysis", 
      "initial conditions", 
      "low energy dynamics", 
      "harmonic balance", 
      "finite amplitude", 
      "chaotic behavior", 
      "strong function", 
      "energy dynamics", 
      "pendulum", 
      "low energy", 
      "energy", 
      "critical value", 
      "rotates", 
      "interesting behavior", 
      "mode", 
      "analytic results", 
      "perturbation theory", 
      "phase mode", 
      "critical amplitude", 
      "careful numerical analysis", 
      "onset of rotation", 
      "dynamics", 
      "interesting results", 
      "high energy", 
      "behavior", 
      "amplitude", 
      "normal modes", 
      "phase", 
      "chaos", 
      "conditions", 
      "results", 
      "analysis", 
      "frequency", 
      "theory", 
      "low energy region", 
      "values", 
      "balance", 
      "energy region", 
      "region", 
      "threshold", 
      "rotation", 
      "function", 
      "onset", 
      "role", 
      "outer pendulum rotate", 
      "pendulum rotate", 
      "Lindstedt\u2013Poincare analysis", 
      "outlying pendulum"
    ], 
    "name": "Role of initial conditions in the dynamics of a double pendulum at low energies", 
    "pagination": "993-1004", 
    "productId": [
      {
        "name": "dimensions_id", 
        "type": "PropertyValue", 
        "value": [
          "pub.1029407189"
        ]
      }, 
      {
        "name": "doi", 
        "type": "PropertyValue", 
        "value": [
          "10.1007/s11071-013-0848-1"
        ]
      }
    ], 
    "sameAs": [
      "https://doi.org/10.1007/s11071-013-0848-1", 
      "https://app.dimensions.ai/details/publication/pub.1029407189"
    ], 
    "sdDataset": "articles", 
    "sdDatePublished": "2022-01-01T18:29", 
    "sdLicense": "https://scigraph.springernature.com/explorer/license/", 
    "sdPublisher": {
      "name": "Springer Nature - SN SciGraph project", 
      "type": "Organization"
    }, 
    "sdSource": "s3://com-springernature-scigraph/baseset/20220101/entities/gbq_results/article/article_590.jsonl", 
    "type": "ScholarlyArticle", 
    "url": "https://doi.org/10.1007/s11071-013-0848-1"
  }
]
 

Download the RDF metadata as:  json-ld nt turtle xml License info

HOW TO GET THIS DATA PROGRAMMATICALLY:

JSON-LD is a popular format for linked data which is fully compatible with JSON.

curl -H 'Accept: application/ld+json' 'https://scigraph.springernature.com/pub.10.1007/s11071-013-0848-1'

N-Triples is a line-based linked data format ideal for batch operations.

curl -H 'Accept: application/n-triples' 'https://scigraph.springernature.com/pub.10.1007/s11071-013-0848-1'

Turtle is a human-readable linked data format.

curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/s11071-013-0848-1'

RDF/XML is a standard XML format for linked data.

curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/s11071-013-0848-1'


 

This table displays all metadata directly associated to this object as RDF triples.

139 TRIPLES      22 PREDICATES      77 URIs      66 LITERALS      6 BLANK NODES

Subject Predicate Object
1 sg:pub.10.1007/s11071-013-0848-1 schema:about anzsrc-for:01
2 anzsrc-for:0101
3 schema:author Nf243a14ace824407978e96dcb0c06592
4 schema:citation sg:pub.10.1007/s11071-007-9270-x
5 sg:pub.10.1007/s11071-012-0378-2
6 sg:pub.10.1007/s12043-009-0099-3
7 schema:datePublished 2013-03-29
8 schema:datePublishedReg 2013-03-29
9 schema:description We consider the low energy dynamics of the double pendulum. Low energy implies energies close to the critical value required to make the outer pendulum rotate. All the known interesting results for the double pendulum are at high energies, that is, energies higher than that required to make both pendulums rotate. We show that interesting behavior can occur at low energies as well by which we mean energies just sufficient to make the outer pendulum rotate. A harmonic balance and the Lindstedt–Poincare analysis at the low energies establish that at small, but finite amplitude; the two normal modes behave differently. While the frequency of the “in-phase” mode is almost unchanged with increasing amplitude, the frequency of the “out-of-phase” mode drops sharply. Numerical analysis verifies this analytic result and since the perturbation theory indicates a mode softening for the out-of-phase mode at a critical amplitude, we did a careful numerical analysis of the low energy region just above the threshold for onset of rotation for the outlying pendulum. We find chaotic behavior, but the chaos is a strong function of the initial condition.
10 schema:genre article
11 schema:inLanguage en
12 schema:isAccessibleForFree false
13 schema:isPartOf N544f5c54344e48668c58b9de85fb6f63
14 Nd57fd62f2f3648cf84d97a7a2982396b
15 sg:journal.1040905
16 schema:keywords Lindstedt–Poincare analysis
17 amplitude
18 analysis
19 analytic results
20 balance
21 behavior
22 careful numerical analysis
23 chaos
24 chaotic behavior
25 conditions
26 critical amplitude
27 critical value
28 double pendulum
29 dynamics
30 energy
31 energy dynamics
32 energy region
33 finite amplitude
34 frequency
35 function
36 harmonic balance
37 high energy
38 initial conditions
39 interesting behavior
40 interesting results
41 low energy
42 low energy dynamics
43 low energy region
44 mode
45 normal modes
46 numerical analysis
47 onset
48 onset of rotation
49 outer pendulum rotate
50 outlying pendulum
51 pendulum
52 pendulum rotate
53 perturbation theory
54 phase
55 phase mode
56 region
57 results
58 role
59 rotates
60 rotation
61 strong function
62 theory
63 threshold
64 values
65 schema:name Role of initial conditions in the dynamics of a double pendulum at low energies
66 schema:pagination 993-1004
67 schema:productId Na3f84a8d368345f79e8f901ef70c4026
68 Nd908809e2964430a8860946137bbcce8
69 schema:sameAs https://app.dimensions.ai/details/publication/pub.1029407189
70 https://doi.org/10.1007/s11071-013-0848-1
71 schema:sdDatePublished 2022-01-01T18:29
72 schema:sdLicense https://scigraph.springernature.com/explorer/license/
73 schema:sdPublisher N65170d36a84e485088c80e77aff4b2ad
74 schema:url https://doi.org/10.1007/s11071-013-0848-1
75 sgo:license sg:explorer/license/
76 sgo:sdDataset articles
77 rdf:type schema:ScholarlyArticle
78 N544f5c54344e48668c58b9de85fb6f63 schema:issueNumber 1-2
79 rdf:type schema:PublicationIssue
80 N65170d36a84e485088c80e77aff4b2ad schema:name Springer Nature - SN SciGraph project
81 rdf:type schema:Organization
82 Na3f84a8d368345f79e8f901ef70c4026 schema:name dimensions_id
83 schema:value pub.1029407189
84 rdf:type schema:PropertyValue
85 Nd57fd62f2f3648cf84d97a7a2982396b schema:volumeNumber 73
86 rdf:type schema:PublicationVolume
87 Nd908809e2964430a8860946137bbcce8 schema:name doi
88 schema:value 10.1007/s11071-013-0848-1
89 rdf:type schema:PropertyValue
90 Nf243a14ace824407978e96dcb0c06592 rdf:first sg:person.016070707602.84
91 rdf:rest Nf61b7f123f654f75ad7b099c981584cd
92 Nf30484364f5a4a838fe7dae4b795ff75 rdf:first sg:person.015365735162.55
93 rdf:rest rdf:nil
94 Nf61b7f123f654f75ad7b099c981584cd rdf:first sg:person.016276051627.98
95 rdf:rest Nf30484364f5a4a838fe7dae4b795ff75
96 anzsrc-for:01 schema:inDefinedTermSet anzsrc-for:
97 schema:name Mathematical Sciences
98 rdf:type schema:DefinedTerm
99 anzsrc-for:0101 schema:inDefinedTermSet anzsrc-for:
100 schema:name Pure Mathematics
101 rdf:type schema:DefinedTerm
102 sg:journal.1040905 schema:issn 0924-090X
103 1573-269X
104 schema:name Nonlinear Dynamics
105 schema:publisher Springer Nature
106 rdf:type schema:Periodical
107 sg:person.015365735162.55 schema:affiliation grid-institutes:grid.450311.2
108 schema:familyName Bhattacharjee
109 schema:givenName Jayanta K.
110 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.015365735162.55
111 rdf:type schema:Person
112 sg:person.016070707602.84 schema:affiliation grid-institutes:grid.452882.1
113 schema:familyName Roy
114 schema:givenName Jyotirmoy
115 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.016070707602.84
116 rdf:type schema:Person
117 sg:person.016276051627.98 schema:affiliation grid-institutes:grid.452759.8
118 schema:familyName Mallik
119 schema:givenName Asok K.
120 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.016276051627.98
121 rdf:type schema:Person
122 sg:pub.10.1007/s11071-007-9270-x schema:sameAs https://app.dimensions.ai/details/publication/pub.1049100526
123 https://doi.org/10.1007/s11071-007-9270-x
124 rdf:type schema:CreativeWork
125 sg:pub.10.1007/s11071-012-0378-2 schema:sameAs https://app.dimensions.ai/details/publication/pub.1049168943
126 https://doi.org/10.1007/s11071-012-0378-2
127 rdf:type schema:CreativeWork
128 sg:pub.10.1007/s12043-009-0099-3 schema:sameAs https://app.dimensions.ai/details/publication/pub.1021542691
129 https://doi.org/10.1007/s12043-009-0099-3
130 rdf:type schema:CreativeWork
131 grid-institutes:grid.450311.2 schema:alternateName Harish-Chandra Research Institute, Jhunsi, 211019, Allahabad, India
132 schema:name Harish-Chandra Research Institute, Jhunsi, 211019, Allahabad, India
133 rdf:type schema:Organization
134 grid-institutes:grid.452759.8 schema:alternateName S. N. Bose National Centre for Basic Science, Salt Lake, 700098, Kolkata, India
135 schema:name S. N. Bose National Centre for Basic Science, Salt Lake, 700098, Kolkata, India
136 rdf:type schema:Organization
137 grid-institutes:grid.452882.1 schema:alternateName UM-DAE Centre for Excellence in Basic Sciences, Santa Cruz(E), 400098, Mumbai, India
138 schema:name UM-DAE Centre for Excellence in Basic Sciences, Santa Cruz(E), 400098, Mumbai, India
139 rdf:type schema:Organization
 




Preview window. Press ESC to close (or click here)


...